Related papers: Unramified Brauer groups and isoclinism

The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramified Brauer group of a given quotient space. We derive a homological version of the Bogomolov multiplier, prove a Hopf-type formula, find a five term exact…

In this paper, we develop the concept of the Bogomolov multiplier for a multiplicative Lie algebra and establish a Hopf-type formula. Consequently, we see that the Bogomolov multipliers of two isoclinic multiplicative Lie algebras are…

We present the unoriented versions of the Schur and Bogomolov multipliers associated with a finite group $G$. We show that the unoriented Schur multiplier is isomorphic to the second cohomology group $H^2(G;\ZZ_2)$. We define the unoriented…

We introduce the $q$-Bogomolov multiplier as a generalization of the Bogomolov multiplier, and we prove that it is invariant under $q$-isoclinism. We prove that the $q$-Schur Multiplier is invariant under $q$- exterior isoclinism, and as an…

We describe the group of braided tensor autoequivalences of the Drinfeld centre of a finite group $G$ isomorphic to the identity functor (just as a functor) as a semi-direct product $Aut^1_{br}(\Z(G))\ \simeq\ Out_{2-cl}(G)\ltimes B(G)\ $…

In this paper we extend the notion of CP covers for groups to the field of Lie algebras, and show that despite the case of groups, all CP covers of a Lie algebra are isomorphic. Finally we show that CP covers of groups and Lie rings which…

Let $G$ be a finite group, $V$ a faithful finite-dimensional representation of $G$ over the complex field $\mathbb{C}$ and $\mathbb{C}(V)^{G}$ be the corresponding invariant field. The Bogomolov multiplier $B_{0}(G)$ of $G$ is canonically…

The Bogomolov multiplier $B_0(G)$ of a finite group $G$ is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of $G$. In this paper we give a positive…

The Bogomolov multiplier $B_0(G)$ of a finite group $G$ is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of $G$. The triviality of the Bogomolov…

The Bogomolov multiplier of a finite group $G$ is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of $G$. This invariant of $G$ plays an important…

The subgroup of the Schur multiplier of a finite group G consisting of all cohomology classes whose restriction to any abelian subgroup of G is zero is called the Bogomolov multiplier of G. We prove that if G is quasisimple or almost…

If $X$ is a locally compact space which admits commuting free and proper actions of locally compact groups $G$ and $H$, then the Brauer groups $\Br_H(G/X)$ and $\Br_G(X/H)$ are naturally isomorphic.

Let $G$ be a finite $p$-group. We prove that whenever the commuting probability of $G$ is greater than $(2p^2 + p - 2)/p^5$, the unramified Brauer group of the field of $G$-invariant functions is trivial. Equivalently, all relations between…

We prove that if $G$ is a finite group, then the exponent of its Bogomolov multiplier divides the exponent of $G$ in the following four cases: (i) $G$ is metabelian, (ii) $\exp G=4$, (iii) $G$ is nilpotent of class $\le 5$, or (iv) $G$ is a…

In the work of Rostami et al., the Bogomolov multiplier of a Lie algebra $L$ over a field $\Omega$ is defined as a particular factor of a subalgebra of the exterior product $L \wedge L$. If $L$ is finite dimensional, we identify this object…

Let $G$ be a $p$-group of maximal class and order $p^n$. We determine whether or not the Bogomolov multiplier $B_0(G)$ is trivial in terms of the lower central series of $G$ and $P_1 = C_G(\gamma_2(G) / \gamma_4(G))$. If in addition $G$ has…

The Bogomolov multiplier $B_0(G)$ of a finite group $G$ is the subgroup of the Schur multiplier $H^2(G,\mathbb Q/\mathbb Z)$ consisting of the cohomology classes which vanish after restricting to every abelian subgroup of $G$. We give a new…

Let $G$ be a finite group. The Bogomolov multiplier $B_0(G)$ is constructed as an obstruction to the rationality of $\bm{C}(V)^G$ where $G\to GL(V)$ is a faithful representation over $\bm{C}$. We prove that, for any finite groups $G_1$ and…

Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.

We introduce the notion of isoclinism between central extensions in the category of algebras with bracket. We provide several equivalent conditions under which algebras with bracket are isoclinic. We also study the connection between…