Related papers: Multiplicative Invariants and Semigroup Algebras

Finite elements, which are well-known and studied in the framework of vector lattices, are investigated in $\ell$-algebras, preferably in $f$-algebras, and in product algebras. The additional structure of an associative multiplication leads…

The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

Let $k$ be an algebraically closed field of characteristic $p>0$, let G=GL_n be the general linear group over $k$, let g=gl_n be its Lie algebra and let $D_s$ be subalgebra of the divided power algebra of g^* spanned by the divided power…

The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…

Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical…

This work is a continuation of Automorphisms of $K$-groups I, P. Flavell, preprint. The main object of study is a finite $K$-group $G$ that admits an elementary abelian group $A$ acting coprimely. For certain group theoretic properties…

In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.

Let X be an affine irreducible variety over an algebraically closed field k of characteristic zero. Given an automorphism F, we denote by k(X)^F its field of invariants, i.e. the set of rational functions f on X such that f(F)=f. Let n(F)…

We study the invariant theory of a class of quantum Weyl algebras under group actions and prove that the fixed subrings are always Gorenstein. We also verify the Tits alternative for the automorphism groups of these quantum Weyl algebras.

The paper is an overview of recent results on algebraic structures (semigroups, groupoids, algebras, inverse semigroups, and groups) associated with objects with a rich set of partial symmetries. We discuss etale groupoids and inverse…

An inverse semigroup $S$ is a semigroup in which every element has a unique inverse in the sense of semigroup theory, that is, if $a \in S$ then there exists a unique $b\in S$ such that $a = aba$ and $b = bab$. We say that an inverse…

For a locally compact group G and a compact subgroup K, the corresponding Hecke algebra consists of all continuous compactly supported complex functions on G that are K-bi-invariant. There are many examples of totally disconnected locally…

An algebra $\A$ is said to be an independence algebra if it is a matroid algebra and every map $\al:X\to A$, defined on a basis $X$ of $\A$, can be extended to an endomorphism of $\A$. These algebras are particularly well behaved…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},\ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$, where…

For every finite unital inverse semigroup $S$ and $S$-$C^*$-algebra $A$ we establish an isomorphism between $KK^S(\mathbb{C},A)$ and $K(A \rtimes S)$. This extends the classical Green--Julg isomorphism from finite groups to finite inverse…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semi-bounded if the corresponding operators $i\dd\pi(x)$ from the derived representations are uniformly bounded from above on some non-empty open subset…

We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…

We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe the free objects in varieties of semilattice ordered algebras…