Abstract
The aim of the paper is to introduce new large classes of algebras—quiver generalized Weyl algebras, skew category algebras, diskew polynomial rings and skew semi-Laurent polynomial rings.
Highlights
In this paper, K is a commutative ring with 1, algebra means a K -algebra
The quiver generalized Weyl algebras Let Q = (Q0, Q1) be a quiver where Q0 is the set of vertices and Q1 is the set of arrows of Q
The functor σ from the double quiver Q to the category of K -algebras is uniquely determined by the ring D = σ (1) and two of its K -algebra endomorphisms σx and σx (we assume that σ (11) = idD)
Summary
K is a commutative ring with 1, algebra means a K -algebra. It is not assumed that a K -algebra has an identity element. Missing definitions can be found in [11]. The aim of the paper is to introduce new large classes of algebras—quiver generalized Weyl algebras, skew category algebras, diskew polynomial rings, skew semi-Laurent polynomial rings and the simplex generalized Weyl algebras
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