Florin Panaite
Given an associative algebra H, a linear space U and some linear maps J, T, γ, ηsatisfying some axioms, we define an associative algebra structure on U\otimes H, called an L-R-crossed product. This contains as particular cases some previous constructions, such as the (iterated) Brzezinski crossed product and the L-R-smash product over quasi-bialgebras.
Florin Panaite
This paper contains 2 sections, 1 theorem, 14 equations.
Theorem 1.1
Let $(H, \mu _H, 1_H)$ be an (associative unital) algebra and $U$ a vector space equipped with a distinguished nonzero element $1_U\in U$. Assume that we are given linear maps (with respective notation) Assume that the following conditions are satisfied, for all $u, u', u"\in U$ and $h, h'\in H$ (we denote by $j$ and $t$ some copies of $J$ and respectively $T$): If we define on $U\otimes H$ a mu
