相关论文: Notes on normed algebras, 2

We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.

A detailed presentation of the results obtained during my Ph.D. research. The main investigations concern explicit descriptions of classes of finite dimensional pointed Hopf algebras and their quasi-isomorphism types.

We classify unital associative conformal algebras of linear growth and provide new examples of such.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent commutative algebras. Our method of classification is based on the standard method of classification of central extensions of smaller…

In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth.

Let $G$ be a finite group. There is a standard theorem on the classification of $G$-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of…

This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.

We study the notion of $\Gamma$-graded commutative algebra for an arbitrary abelian group $\Gamma$. The main examples are the Clifford algebras already treated by Albuquerque and Majid. We prove that the Clifford algebras are the only…

We study bimodule quantum Riemannian geometries over the field $\Bbb F_2$ of two elements as the extreme case of a finite-field adaptation of noncommutative-geometric methods for physics. We classify all parallelisable such geometries for…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.

We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also…

In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called…

We make some remarks on deformations over non-commutative base. We describe the base algebra of versal deformations using $T^1$ and $T^2$.

In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary $2$-representations of finitary $2$-categories.

We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.

A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…

The metohod of ortogonal rotations introduced in the previous papers of the author is used for construction of the explicit form the generators of the simple roots for quantum (and ussual) semisimple algebras. All calculations are presented…

We present explicit examples finite tensor categories that are C_2-graded extensions of the corepresentation category of certain finite-dimensional non-semisimple Hopf algebras.

Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.