Unit group of semisimple group algebras of some non-metabelian groups of order 120

In this paper, we give the characterization of the unit groups of semisimple group algebras of some non-metabelian groups of order 120. This study completes the study of unit groups of semisimple group algebras of all groups up to order 120, except that of the symmetric group [Formula: see text] and groups of order 96.

Finiteness of ℚ-Fano Compactifications of Semisimple Groups with Kähler–Einstein Metrics

Let $G$ be a complex semisimple group. In this note, we give a method to classify $\mathbb Q$-Fano compactifications of $G$. We will prove that there are only finitely many $\mathbb Q$-Fano $G$-compactifications that admit (singular) Kähler–Einstein metrics. As an application, this improves a former result in [ 19].

Quantum Principal Bundles on Projective Bases

The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study noncommutative principal bundles corresponding to $$G \rightarrow G/P$$ G → G / P , where G is a semisimple group and P a parabolic subgroup.

On the holomorph of finite semisimple groups

Given a finite nonabelian semisimple group 𝐺, we describe those groups that have the same holomorph as 𝐺, that is, those regular subgroups N\simeq G of S(G), the group of permutations on the set 𝐺, such that N_{S(G)}(N)=N_{S(G)}(\rho(G)), where 𝜌 is the right regular representation of 𝐺.

Zero-divisor graph of semisimple group-rings

Let [Formula: see text], [Formula: see text], [Formula: see text] denote the zero-divisor graph, compressed zero-divisor graph and annihilating ideal graph of a commutative ring [Formula: see text], respectively. In this paper, we prove that [Formula: see text] for a semisimple commutative ring [Formula: see text] and represent [Formula: see text] as a generalized join of a finite set of graphs. Further, we study the zero-divisor graph of a semisimple group-ring [Formula: see text] and proved several structural properties of [Formula: see text] and [Formula: see text], where [Formula: see text] is a field with [Formula: see text] elements and [Formula: see text] is a cyclic group with [Formula: see text] elements.

Good codes from metacyclic groups II

In this paper, we consider semisimple group algebras [Formula: see text] of split metacyclic groups over finite fields. We construct left codes in [Formula: see text] in the case when the order [Formula: see text] is [Formula: see text], where [Formula: see text] and [Formula: see text] are different primes such that [Formula: see text] extend the construction described in a previous paper, determine their dual codes and find some good codes.