Liu, Ling; Guo, Qiao-Ling On twisted smash products of monoidal Hom-Hopf algebras. (English) Zbl 1351.16034 Commun. Algebra 44, No. 10, 4140-4164 (2016). Summary: Let \((H,\alpha)\) be a monoidal Hom-Hopf algebra and \((A,\beta)\) be an \((H,\alpha)\)-Hom-bimodule algebra. In this article, we first introduce the notion of a twisted Hom-smash product \(A*H\) and then find some sufficient and necessary conditions making it into a monoidal Hom-bialgebra. Furthermore, we give a Maschke-type theorem for the twisted Hom-smash product over a semisimple monoidal Hom-Hopf algebra \((H,\alpha)\). Finally, we form an associated Morita context \([A^{biH},{_{A^{biH}}A_{A*H}},{_{A*H}A}_{A^{biH}},A*H]\) in the category \(\widetilde{\mathcal H}(\mathcal M_k)\). Cited in 1 Document MSC: 16T05 Hopf algebras and their applications 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 16S40 Smash products of general Hopf actions 16T10 Bialgebras Keywords:monoidal Hom-Hopf algebras; Maschke-type theorems; Morita contexts; twisted Hom-smash products; Hom-bimodule algebras PDFBibTeX XMLCite \textit{L. Liu} and \textit{Q.-L. Guo}, Commun. Algebra 44, No. 10, 4140--4164 (2016; Zbl 1351.16034) Full Text: DOI References: [1] DOI: 10.1080/00927872.2010.490800 · Zbl 1255.16032 [2] Chen Y. Y., J. Math. Phys 54 pp 1– (2013) [3] DOI: 10.1016/0021-8693(86)90082-7 · Zbl 0591.16005 [4] DOI: 10.1080/00927879408825158 · Zbl 0821.16038 [5] Drinfeld, V. G. (1986).Quantum Groups. Proceedings of the International Congress of Mathematicians. Berkeley, pp.798–820. [6] DOI: 10.4303/jglta/S090402 · Zbl 1237.17005 [7] DOI: 10.1016/j.jalgebra.2010.05.003 · Zbl 1236.17003 [8] DOI: 10.4303/jglta/S070206 · Zbl 1184.17002 [9] DOI: 10.1007/978-3-540-85332-9_17 · Zbl 1173.16019 [10] DOI: 10.1142/S0219498810004117 · Zbl 1259.16041 [11] DOI: 10.1016/0021-8693(77)90208-3 · Zbl 0353.16004 [12] DOI: 10.1090/cbms/082 [13] DOI: 10.1006/jabr.1994.1033 · Zbl 0801.16039 [14] DOI: 10.1080/00927879808826288 · Zbl 0912.16021 [15] DOI: 10.1081/AGB-120028788 · Zbl 1079.16030 [16] DOI: 10.1360/012011-138 [17] Yau D., J. Lie Theory 19 pp 409– (2009) [18] Yau D., Int. Electron. J. Algebra 8 pp 45– (2010) [19] DOI: 10.1088/1751-8113/45/6/065203 · Zbl 1241.81110 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.