Related papers: Cubic algebras and Implication Algebras
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicative-orthomodular algebras, and give characterizations of these…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras,…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
It is known that any multiplication of a finite dimensional algebra is determined by a matrix of structural constants. In general, this is a cubic matrix. Difficulty of investigation of an algebra depends on the cubic matrix. Such a cubic…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.
The concept of a quantum algebra is made easy through the investigation of the prototype algebras $u_{qp}(2)$, $su_q(2)$ and $u_{qp}(1,1)$. The latter quantum algebras are introduced as deformations of the corresponding Lie algebras~; this…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
We consider simple cusp algebras, that is certain subalgebras of the algebra of holomorphic functions on a disk that are annihilated by some distributions living on a singleton. We determine when these algebras can be holized in two…
We construct algebras from rhombohedral tilings of Euclidean space obtained as projections of certain cubical complexes. We show that these `Cubist algebras' satisfy strong homological properties, such as Koszulity and quasi-heredity,…
We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…
Recent developments of Baxter algebras have lead to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first kind and the second kind, partitions and multinomial…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
The input and output algebras of an infinite qubit system and their representations are described.
We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. We focus on generalizations of cluster algebras and…