Andreas Cap, Hermann Schichl, Jiri Vanzura
On Twisted Tensor Products of Algebras
The paper is published: Commun. Algebra 23, 12 (1995) 4701-4735

MSC:

16E40 Hochschild and other homology and cohomology theories for rings

16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)

16S35 Twisted and skew group rings, crossed products

16S80 Deformations of rings, See also {14D15}

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

Abstract: The problems considered in this paper are motivated by
non-commutative geometry.
Starting from two unital algebras $A$ and $B$ over a commutative ring
$\Bbb K$ we describe all triples $(C,i_A,i_B)$, where $C$ is a unital
algebra and $i_A$ and $i_B$ are inclusions of $A$ and $B$ into $C$
such that the canonical linear map $(i_A,i_B):A\otimes B\to C$ is a
linear isomorphism. We discuss possibilities to construct
differential forms and modules over $C$ from differential forms and
modules over $A$ and $B$, and give a description of deformations of
such structures using cohomological methods.

Keywords: Non-commutative geometry, twisted tensor products, twisting maps