相关论文: Affine algebraic monoids as endomorphisms' monoids…

Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have…

For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discretization is isomorphic to the limit of certain perfect…

It is shown that a finite monoid can have an infinite irredundant basis of equations.

We give a universal construction of a derived affine group scheme and its representation category from a symmetric monoidal infinity-category, which we shall call the tannnakization of a symmetric monoidal infinity-category. This can be…

The class of finitely presented algebras over a field K with a set of generators a_1,...,a_n and defined by homogeneous relations of the form a_1a_2...a_n = a_{sigma(1)}a_{sigma(2)}...a_{sigma(n)}, where sigma runs through an abelian…

In this paper, we classify the finite dimensional irreducible modules for affine BMW algebra over an algebraically closed field with arbitrary characteristic.

A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. An algebra is said to be affine complete if every congruence preserving function is a polynomial…

We outline a new approach to classify real forms and automorphisms of finite order of affine Kac-Moody algebras.

A connected component of an affine algebraic group is called periodic if all its elements have finite order. We give a characterization of periodic components in terms of automorphisms with finite number of fixed points. It is also…

We present some fundamental results on (possibly nonlinear) algebraic semigroups and monoids. These include a version of Chevalley's structure theorem for irreducible algebraic monoids, and the description of all algebraic semigroup…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain…

We construct a monomial basis of the positive part of the quantized enveloping algebra associated to a finite-dimensional simple Lie algebra. As an application we give a simple proof of the existence and uniqueness of the canonical basis of…

The aim of this paper is sketch a theory of divisibility and factorisation in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely…

We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

In this note, we show that the epimorphic subgroups of an algebraic group are exactly the pull-backs of the epimorphic subgroups of its affinization. We also obtain epimorphicity criteria for subgroups of affine algebraic groups, which…

We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.

We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…

Necessary and sufficient conditions are given for the endomorphism monoid of a profinite semigroup to be profinite. A similar result is established for the automorphism group.