zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities. (English) Zbl 1099.17015
The authors first introduce the notion of quasi-hom-Lie algebras, a natural generalization of hom-Lie algebras introduced by J. T. Hartwig and the authors. Quasi-hom-Lie algebras include color Lie algebras and superalgebras, and can be seen as deformations of these by maps, twisting the Jacobi identity and skew-symmetry. The goal for introducing the quasi-hom-Lie algebras is to generalize or deform the Witt algebra of derivations on the Laurent polynomials ${\Bbb C}[t,t^{-1}]$. A theory of central extensions for quasi-hom-Lie algebras is developed. The main result of the paper is the description of central extensions of quasi-hom-Lie algebras in terms of equivalence classes of 2-cocycle-like maps.
Reviewer: Yucai Su (Hefei)

MSC:
17B99Lie algebras
17B68Virasoro and related algebras
WorldCat.org
Full Text: DOI arXiv
References:
[1] Aizawa, N.; Sato, H. -T.: Q-deformation of the Virasoro algebra with central extension. Phys. lett. B 256, No. 2, 185-190 (1999)
[2] Bloch, S.: Zeta values and differential operators on the circle. J. algebra 182, 476-500 (1996) · Zbl 0868.17017
[3] Chaichian, M.; Isaev, A. P.; Lukierski, J.; Popowicz, Z.; Prešnajder, P.: Q-deformations of Virasoro algebra and conformal dimensions. Phys. lett. B 262, No. 1, 32-38 (1991)
[4] Chaichian, M.; Kulish, P.; Lukierski, J.: Q-deformed Jacobi identity, q-oscillators and q-deformed infinite-dimensional algebras. Phys. lett. B 237, No. 3 -- 4, 401-406 (1990)
[5] Chaichian, M.; Prešnajder, P.: Q-Virasoro algebra, q-conformal dimensions and free q-superstring. Nuclear phys. B 482, No. 1 -- 2, 466-478 (1996) · Zbl 0974.81507
[6] Chung, W. -S.: Two parameter deformation of Virasoro algebra. J. math. Phys. 35, No. 5, 2490-2496 (1994) · Zbl 0822.17015
[7] Curtright, T. L.; Zachos, C. K.: Deforming maps for quantum algebras. Phys. lett. B 243, No. 3, 237-244 (1990)
[8] Deligne, P.; Etingof, P.; Freed, D. S.; Jeffrey, L. C.; Kazhdan, D.; Morgan, J. W.; Morrison, D. R.; Witten, E.: Quantum fields and strings: A course for mathematicians. 2 (1999) · Zbl 0984.00503
[9] Di Francesco, P.; Mathieu, P.; Sénéchal, D.: Conformal field theory. (1997) · Zbl 0869.53052
[10] Frenkel, I.; Lepowsky, J.; Meurman, A.: Vertex operator algebras and the monster. (1988) · Zbl 0674.17001
[11] Fuchs, J.: Affine Lie algebras and quantum groups. (1992) · Zbl 0925.17031
[12] Fuchs, J.: Lectures on conformal field theory and Kac -- Moody algebras. Springer lecture notes in phys. 498 (1997)
[13] Fuks, D. B.: Cohomology of infinite-dimensional Lie algebras. (1986) · Zbl 0667.17005
[14] Hartwig, J. T.; Larsson, D.; Silvestrov, S. D.: Deformations of Lie algebras using $\sigma $-derivations · Zbl 1138.17012
[15] Hellström, L.; Silvestrov, S. D.: Commuting elements in q-deformed Heisenberg algebras. (2000) · Zbl 0956.17006
[16] H.P. Jakobsen, Matrix chain models and their q-deformations, Preprint Mittag-Leffler Institute, Report Nr. 23, 2003/2004, ISSN 1103-467X, ISRN IML-R-23-03/04-SE
[17] Jakobsen, H. P.; Lee, H. C. -W.: Matrix chain models and Kac -- Moody algebras. Contemp. math. 343, 147-165 (2004) · Zbl 1142.17307
[18] Kac, V. G.: Simple irreducible graded Lie algebras of finite growth. Math. USSR izv. 2, 1271-1311 (1968) · Zbl 0222.17007
[19] Kac, V. G.; Raina, A. K.: Highest weight representations of infinite-dimensional Lie algebras. (1987) · Zbl 0668.17012
[20] Kassel, C.: Cyclic homology of differential operators, the Virasoro algebra and a q-analogue. Comm. math. Phys. 146, 343-351 (1992) · Zbl 0761.17020
[21] Khesin, B.; Lyubashenko, V.; Roger, C.: Extensions and contractions of Lie algebra of q-pseudodifferential symbols on the circle. J. func. Anal. 143, 55-97 (1997) · Zbl 0872.35138
[22] Larsson, D.; Silvestrov, S. D.: Quasi-Hom-Lie algebras, central extensions and 2-cocycle-like identities
[23] Li, W. -L.: 2-cocycles on the algebra of differential operators. J. algebra 122, 64-80 (1989) · Zbl 0671.17010
[24] Moody, R. V.: A new class of Lie algebras. J. algebra 10, 211-230 (1968) · Zbl 0191.03005
[25] Passman, D. S.: Simple Lie color algebras of Witt type. J. algebra 208, 698-721 (1998) · Zbl 0923.17013
[26] Polychronakos, A. P.: Consistency conditions and representations of a q-deformed Virasoro algebra. Phys. lett. B 256, No. 1, 35-40 (1991)
[27] Sato, H. -T.: Realizations of q-deformed Virasoro algebra. Progr. theoret. Phys. 89, No. 2, 531-544 (1993)
[28] Sato, H. -T.: Q-Virasoro operators from an analogue of the Noether currents. Z. phys. C 70, No. 2, 349-355 (1996)
[29] Scheunert, M.: Introduction to the cohomology of Lie superalgebras and some applications. Res. exp. Math. 25, 77-107 (2002) · Zbl 1022.17013
[30] Scheunert, M.; Zhang, R. B.: Cohomology of Lie superalgebras and their generalizations. J. math. Phys. 39, 5024-5061 (1998) · Zbl 0928.17023