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Kachalova, M. A.

Hochschild cohomology ring for self-injective algebras of tree class \(E_8\). (English. Russian original) Zbl 07688753

J. Math. Sci., New York 272, No. 3, 418-443 (2023); translation from Zap. Nauchn. Semin. POMI 500, 112-148 (2021).
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:  16E40 16E05 16G10
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\textit{M. A. Kachalova}, J. Math. Sci., New York 272, No. 3, 418--443 (2023; Zbl 07688753); translation from Zap. Nauchn. Semin. POMI 500, 112--148 (2021)
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Generalov, A. I.

Hochschild cohomology for algebras of semidihedral type. X: Cohomology algebra for the exceptional local algebras. (English. Russian original) Zbl 07688752

J. Math. Sci., New York 272, No. 3, 376-417 (2023); translation from Zap. Nauchn. Semin. POMI 500, 51-111 (2021).
Reviewer: Burkhard Külshammer (Jena)
MSC:  16E40 16E05
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\textit{A. I. Generalov}, J. Math. Sci., New York 272, No. 3, 376--417 (2023; Zbl 07688752); translation from Zap. Nauchn. Semin. POMI 500, 51--111 (2021)
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Das, Biswarup; Franz, Uwe; Kula, Anna; Skalski, Adam

Second cohomology groups of the Hopf\(^*\)-algebras associated to universal unitary quantum groups. (Deuxièmes groupes de cohomologie des algèbres de Hopf\(^*\) involutives associées aux groupes quantiques unitaires universels.) (English. French summary) Zbl 1517.16006

Ann. Inst. Fourier 73, No. 2, 479-509 (2023).
MSC:  16E40 16T20
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\textit{B. Das} et al., Ann. Inst. Fourier 73, No. 2, 479--509 (2023; Zbl 1517.16006)
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Wang, Jinmin; Xie, Zhizhang; Yu, Guoliang

\(\ell^1\)-higher index, \(\ell^1\)-higher rho invariant and cyclic cohomology. (English) Zbl 1509.19009

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 535-579 (2023).
MSC:  19K56 19D55
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\textit{J. Wang} et al., Proc. Symp. Pure Math. 105, 535--579 (2023; Zbl 1509.19009)
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van Nuland, Teun D. H.; van Suijlekom, Walter D.

Cyclic cocycles and one-loop corrections in the spectral action. (English) Zbl 07675046

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 513-533 (2023).
MSC:  81S10 37A20 58J28 53C21 16E40 41A58 47A10
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\textit{T. D. H. van Nuland} and \textit{W. D. van Suijlekom}, Proc. Symp. Pure Math. 105, 513--533 (2023; Zbl 07675046)
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Tsygan, Boris

On noncommutative crystalline cohomology. (English) Zbl 07675045

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 491-511 (2023).
MSC:  16E40 16S38
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\textit{B. Tsygan}, Proc. Symp. Pure Math. 105, 491--511 (2023; Zbl 07675045)
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Puschnigg, Michael

Periodic cyclic homology of crossed products. (English) Zbl 07675042

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 435-455 (2023).
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:  16E40 18G35 20J06
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\textit{M. Puschnigg}, Proc. Symp. Pure Math. 105, 435--455 (2023; Zbl 07675042)
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Ponge, Raphaël

Cyclic homology and group actions. (English) Zbl 1509.19006

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 371-395 (2023).
MSC:  19D55 20J06 55N91
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\textit{R. Ponge}, Proc. Symp. Pure Math. 105, 371--395 (2023; Zbl 1509.19006)
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Pflaum, Markus J.

Localization in Hochschild homology. (English) Zbl 07675039

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 353-369 (2023).
MSC:  16E40 14P99 18G99 55N30
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\textit{M. J. Pflaum}, Proc. Symp. Pure Math. 105, 353--369 (2023; Zbl 07675039)
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Moscovici, Henri

On the van Est analogy in Hopf cyclic cohomology. (English) Zbl 07675037

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 297-310 (2023).
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:  16E40 57R32 58B34
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\textit{H. Moscovici}, Proc. Symp. Pure Math. 105, 297--310 (2023; Zbl 07675037)
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Meyer, Ralf; Mukherjee, Devarshi

Local cyclic homology for nonarchimedean Banach algebras. (English) Zbl 1509.19005

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 281-295 (2023).
MSC:  19D55
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\textit{R. Meyer} and \textit{D. Mukherjee}, Proc. Symp. Pure Math. 105, 281--295 (2023; Zbl 1509.19005)
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Khalkhali, Masoud; Shapiro, Ilya

Hopf cyclic cohomology and beyond. (English) Zbl 1516.19001

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 211-237 (2023).
Reviewer: Jerry M. Lodder (Las Cruces)
MSC:  19D55 16E40 16T05 18D15
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\textit{M. Khalkhali} and \textit{I. Shapiro}, Proc. Symp. Pure Math. 105, 211--237 (2023; Zbl 1516.19001)
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Hesselholt, Lars

Topological cyclic homology and the Fargues-Fontaine curve. (English) Zbl 1509.11112

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 197-210 (2023).
MSC:  11S70 19D55 14F30
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\textit{L. Hesselholt}, Proc. Symp. Pure Math. 105, 197--210 (2023; Zbl 1509.11112)
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Gepner, David

Algebraic \(K\)-theory and generalized stable homotopy theory. (English) Zbl 1511.55012

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 161-184 (2023).
MSC:  55P42 19D55 18N60 55U40
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\textit{D. Gepner}, Proc. Symp. Pure Math. 105, 161--184 (2023; Zbl 1511.55012)
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Dundas, Bjørn Ian

Applications of topological cyclic homology to algebraic \(K\)-theory. (English) Zbl 1509.19004

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 135-159 (2023).
MSC:  19D55
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\textit{B. I. Dundas}, Proc. Symp. Pure Math. 105, 135--159 (2023; Zbl 1509.19004)
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Cuntz, Joachim

The image of Bott peridocity in cyclic homology. (English) Zbl 1508.19004

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 123-134 (2023).
MSC:  19D55 19E20 19K35 58B34
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\textit{J. Cuntz}, Proc. Symp. Pure Math. 105, 123--134 (2023; Zbl 1508.19004)
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Connes, Alain; Consani, Caterina

Hochschild homology, trace map and \(\zeta\)-cycles. (English) Zbl 07675026

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 83-101 (2023).
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:  11M55 11M06 16E40 11F72 58B34
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\textit{A. Connes} and \textit{C. Consani}, Proc. Symp. Pure Math. 105, 83--101 (2023; Zbl 07675026)
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Block, Jonathan; Higson, Nigel; Sanchez, Jesus jun.

On Perrot’s index cocycles. (English) Zbl 1508.19003

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 29-62 (2023).
MSC:  19D55 19K56 58J40
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\textit{J. Block} et al., Proc. Symp. Pure Math. 105, 29--62 (2023; Zbl 1508.19003)
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Baldare, Alexandre; Benameur, Moulay; Nistor, Victor

Chern-Connes-Karoubi character isomorphisms and algebras of symbols of pseudodifferential operators. (English) Zbl 07675023

Connes, A. (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 105, 1-27 (2023).
MSC:  46L80 19D55 16E40 47L80
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\textit{A. Baldare} et al., Proc. Symp. Pure Math. 105, 1--27 (2023; Zbl 07675023)
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Connes, A. (ed.); Consani, C. (ed.); Dundas, B. I. (ed.); Khalkhali, M. (ed.); Moscovici, H. (ed.)

Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 – October 1, 2021. (English) Zbl 1507.19001

Proceedings of Symposia in Pure Mathematics 105. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-6977-1/pbk; 978-1-4704-7263-4/ebook). x, 579 p. (2023).
MSC:  19-06 19D55 19-03 01A60 01A61 00B25
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\textit{A. Connes} (ed.) et al., Cyclic cohomology at 40. Achievements and future prospects. Proceedings of the conference, virtual, Toronto, ON, Canada, September 27 -- October 1, 2021. Providence, RI: American Mathematical Society (AMS) (2023; Zbl 1507.19001)
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