Related papers: Extensions of the tensor algebra and their applica…

Following arXiv:0909.5586 and arXiv:1411.4125, we construct two super-extensions of the usual tensor algebra through the super-actions of symmetric groups and Hecke algebras respectively. For each extension, we consider a special type of…

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…

The study of derivations and their generalizations on non-associative algebras has proven to be fundamental in understanding the internal symmetries and algebraic dynamics of such structures. In this paper, we investigate derivations and…

Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…

Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies the role played by the integral counterpart of the…

We study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of…

Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…

We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing…

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.

We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra that acts on it and embed their direct sum into an auxiliary algebra. Viewed as endomorphisms of this algebra, we associate adjoint operators to tensors. We…

We consider the Casimir Invariants related to some a special kind of Lie-algebra extensions, called universal extensions. We show that these invariants can be studied using the equivalence between the universal extensions and the…

This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds . Key notions such as the extension and generalization…

The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

Examples of operator algebras with involution include the operator $*$-algebras occurring in noncommutative differential geometry studied recently by Mesland, Kaad, Lesch, and others, several classical function algebras, triangular matrix…

Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index…

This paper presents a $q$-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori-Hecke algebra type $A$ of infinite degree. Namely this…