We introduce the notion of a crossed product of an algebra by a coalgebra C, which generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf algebras. The result of such a crossed product is an algebra which is also a right C-comodule. We find the necessary and sufficient conditions for two coalgebra crossed products be equivalent. We show that the two-dimens...

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative geometry and particle systems with generalized statistics are indicated. PACS. 02. 40. +m Differential geometry in theoretical physics. PACS. 03. 65. Fd Algebr...

We introduce a more general version of the so-called L-R-smash product and study its relations with other kinds of crossed products (two-sided smash and crossed product and diagonal crossed product).

We introduce a more general version of the so-called L-R-smash product and study its relations with other kinds of crossed products (two-sided smash and crossed product and diagonal crossed product). We also give an interpretation of the L-R-smash product in terms of an L-R-twisting datum.

The notion of crossed product with a coquasi-Hopf algebra H is introduced and studied. The result of such a crossed product is an algebra in the monoidal category of right H-comodules. We give necessary and sufficient conditions for two crossed products to be equivalent. Then, two structure theorems for coquasi Hopf modules are given. First, these are relative Hopf modules over the crossed prod...

In this work we present a new definition to the Partial Crossed Product by actions of inverse semigroups in a C-algebra, without using the covariant representations as Sieben did in [5]. Also we present an isomorphism between the partial crossed products by partial actions of a group G and the partial crossed product by actions of S(G), an inverse semigroup associated to G introduced by Exel in...