Related papers: On the unitary subgroup of modular group algebras

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…

We characterize those modular group algebras FG whose group of unitary units is locally nilpotent under the classical involution of FG.

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and $*$ the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all…

Let $U(KG)$ be the group of units of the group ring $KG$ of the group $G$ over a commutative ring $K$. The anti-automorphism $g\mapsto g\m1$ of $G$ can be extended linearly to an anti-automorphism $a\mapsto a^*$ of $KG$. Let $S_*(KG)=\{x\in…

Let $KG$ be the group ring of a group $G$ over a commutative ring $K$ with unity. The rings $KG$ are described for which $xx^\sigma=x^\sigma x$ for all $x=\sum_{g\in G}\alpha_gg\in KG$, where \quad $x\mapsto x^\sigma=~\sum_{g\in…

Let p be an odd prime, F the field of p elements and G a finite abelian p-group with an arbitrary involutory automorphism. Extend this automorphism to the group algebra FG and consider the unitary and the symmetric normalized units of FG.…

Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this extension…

Let F be the field of two elements and G a finite abelian 2-group with an involutory automorphism. The extension of this automorphism to the group algebra FG is called an involutory involution. This determines the groups of unitary and…

Let KG be a group algebra of a finite p-group G over a finite field K of characteristic p. We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group…

In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this…

Let $RG$ be the gruop ring of the group $G$ over ring $R$ and $\mathscr{U}(RG)$ be its unit group. Finding the structure of the unit group of a finite group ring is an old topic in ring theory. In, G. Tang et al: Unit Groups of Group…

The Hilbert manifold $\Sigma$ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits $\Omega\subset \Sigma$ is studied from the topological and metric…

Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V(KG) be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V(KG)…

Consider a finite group $G$ acting on a graded Noetherian $k$-algebra $S$, for some field $k$ of characteristic $p$; for example $S$ might be a polynomial ring. Regard $S$ as a $kG$-module and consider the multiplicity of a particular…

We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of…

Let p be a prime, G a locally finite p-group, K a commutative ring of characteristic p. The anti-automorphism g\mapsto g\m1 of G extends linearly to an anti-automorphism a\mapsto a^* of KG. An element a of KG is called symmetric if a^*=a.…

I argue that the gauge group of noncommutative gauge theory consists of maps into unitary operators on Hilbert space of the form $u=1+K$ with $K$ compact. Some implications of this proposal are outlined.

Let $FG$ be the group algebra of a finite $2$-group $G$ over a finite field $F$ of characteristic two and $\circledast$ an involution which arises from $G$. The $\circledast$-unitary subgroup of $FG$, denoted by $V_{\circledast}(FG)$, is…

We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on some classes of associative algebras, including unital algebras, the semigroup algebras of rectangular bands, algebras with enough…