Semantic Scholar Open Access 2002 36 sitasi

Injective Hopf bimodules, cohomologies of infinite dimensional Hopf algebras and graded-commutativity of the Yoneda product

R. Taillefer

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Abstrak

Abstract We prove that the category of Hopf bimodules over any Hopf algebra has enough injectives, which enables us to extend some results on the unification of Hopf bimodule cohomologies of [R. Taillefer, PhD thesis, 2001; arXiv preprint math.QA/0005019 ] to the infinite dimensional case. We also prove that the cup-product defined on these cohomologies is graded-commutative. Unlike the algebra case (see [S. Schwede, J. Reine Angew. Math. 498 (1998) 153–172]), these methods do not give a non-trivial Gerstenhaber algebra structure on the cohomology we consider. We also comment that the other approach to finding such a structure that we know of (see [M. Farinati, A. Solotar, arXiv preprint math.KT/0207243 ]) also gives a trivial Gerstenhaber algebra structure.

Topik & Kata Kunci

Mathematics

Penulis (1)

R. Taillefer

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Taillefer, R. (2002). Injective Hopf bimodules, cohomologies of infinite dimensional Hopf algebras and graded-commutativity of the Yoneda product. https://doi.org/10.1016/J.JALGEBRA.2004.01.024

Akses Cepat

Lihat di Sumber doi.org/10.1016/J.JALGEBRA.2004.01.024

Informasi Jurnal

Tahun Terbit: 2002
Bahasa: en
Total Sitasi: 36×
Sumber Database: Semantic Scholar
DOI: 10.1016/J.JALGEBRA.2004.01.024
Akses: Open Access ✓