In this paper we prove the universal property of skew PBW extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew PBW extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Art...

In this paper, first we give the notion of a representation relative Rota-Baxter Lie algebra and introduce cohomologies with coefficients in representation. Then classify abelian extensions algebras using second cohomology group, skeletal 2-algebras third group as applications. At last, established general framework representations algebras, which is consistent associative literature, Applicati...

We use fermionic representations to obtain a class of BC N -graded Lie algebras coordinatized by quantum tori with nontrivial central extensions. 0 Introduction Lie algebras graded by the reduced finite root systems were first introduced by Berman-Moody [BM] in order to understand the generalized intersection matrix algebras of Slodowy. [BM] classified Lie algebras graded by the root systems of...

We develop the method for constructing Lax representations of PDEs via twisted extensions their algebras contact symmetries by generalizing construction to Lie--Rinehart algebras. present examples application proposed technique.

Factor systems are a tool for working on the extension problem of algebraic structures such as groups, Lie algebras, and associative algebras. Their applications numerous well-known in these common settings. We construct P algebra analogues to series results from W. R. Scott’s Group Theory, which gives an explicit theory factor group case. Here ranges over Leibniz, Zinbiel, diassociative, dendr...

The review is devoted to nonassociative algebras, rings and modules over them. main actual recent trends in this area are described. Works reviewed on radicals rings, algebras related with skew polynomials, commutative their modules, cyclic obtained as extensions, Ore extensions of hom-associative them, von Neumann finiteness for algebras. Furthermore, there outlined them harmonic analysis nonl...

Bundles of C*-algebras can be used to represent limits physical theories whose algebraic structure depends on the value a parameter. The primary example is [Formula: see text] limit quantities in quantum theories, represented framework strict deformation quantization. In this paper, we understand such limiting procedures terms extension bundle some We prove existence and uniqueness results for ...