let $h$ be a hopf algebra and $a$ an $h$-bimodule algebra‎. ‎in this paper‎, ‎we investigate gorenstein global dimensions for hopf‎ ‎algebras and twisted smash product algebras $astar h$‎. ‎results from‎ ‎the literature are generalized‎.

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎. 

We give some applications of a Hopf algebra constructed from a group acting on another Hopf algebra A as Hopf automorphisms, namely Molnar’s smash coproduct Hopf algebra. We find connections between the exponent and Frobenius-Schur indicators of a smash coproduct and the twisted exponents and twisted Frobenius-Schur indicators of the original Hopf algebra A. We study the category of modules of ...

A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α, β : A → A such that α(a)(bc) = (ab)β(c), for all a, b, c ∈ A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new ...

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors, and prove that they are enough for building an iterated product of any number of fact...