Simple objects in equivariantized module categories

2019 ◽  
Vol 18 (01) ◽  
pp. 1950001
Author(s):  
Sara Pinter ◽  
Virgínia Rodrigues
Keyword(s):  
Finite Group ◽  
Direct Summand ◽  
Indecomposable Module ◽  
Simple Object ◽  
Fusion Category ◽  
Module Category ◽  
Bijective Correspondence ◽  
Isomorphism Classes ◽  
Projective Representations ◽  
A Finite Group

Let [Formula: see text] be a finite group acting on a fusion category [Formula: see text] and let [Formula: see text] be a subgroup of [Formula: see text]. Let [Formula: see text] be a semisimple indecomposable module category over [Formula: see text]. Considering [Formula: see text] a simple object in [Formula: see text] and [Formula: see text] the stabilizer (or inertia) subgroup of [Formula: see text], we establish a bijective correspondence between isomorphism classes of simple objects in equivariantizations [Formula: see text] and [Formula: see text], where such simple objects contain [Formula: see text] as a direct summand. Also, as an application to projective representations of [Formula: see text], we relate isomorphism classes of simple objects in [Formula: see text] with irreducible projective representations of [Formula: see text].

scholarly journals Equivariant Map Queer Lie Superalgebras

2016 ◽  
Vol 68 (2) ◽  
pp. 258-279 ◽  
Author(s):  
Lucas Calixto ◽  
Adriano Moura ◽  
Alistair Savage
Keyword(s):  
Finite Group ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Equivariant Map ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Regular Maps ◽  
A Finite Group ◽  
Special Case

AbstractAn equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) X to a queer Lie superalgebra q that are equivariant with respect to the action of a finite group Γ acting on X and q. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that Γ is abelian and acts freely on X. We show that such representations are parameterized by a certain set of Γ-equivariant finitely supported maps from X to the set of isomorphism classes of irreducible finite-dimensional representations of q. In the special case where X is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.

scholarly journals THE DUAL STRUCTURE OF CROSSED PRODUCT -ALGEBRAS WITH FINITE GROUPS

2013 ◽  
Vol 88 (2) ◽  
pp. 243-249 ◽  
Author(s):  
FIRUZ KAMALOV
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Orbit Space ◽  
Crossed Product ◽  
Irreducible Representations ◽  
Natural Action ◽  
Dual Structure ◽  
Projective Representations ◽  
A Finite Group ◽  
Sigma G

AbstractWe study the space of irreducible representations of a crossed product ${C}^{\ast } $-algebra ${\mathop{A\rtimes }\nolimits}_{\sigma } G$, where $G$ is a finite group. We construct a space $\widetilde {\Gamma } $ which consists of pairs of irreducible representations of $A$ and irreducible projective representations of subgroups of $G$. We show that there is a natural action of $G$ on $\widetilde {\Gamma } $ and that the orbit space $G\setminus \widetilde {\Gamma } $ corresponds bijectively to the dual of ${\mathop{A\rtimes }\nolimits}_{\sigma } G$.

RECOGNIZING BY ORDER AND DEGREE PATTERN OF SOME PROJECTIVE SPECIAL LINEAR GROUPS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250051 ◽  
Author(s):  
B. AKBARI ◽  
A. R. MOGHADDAMFAR
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Linear Groups ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
Isomorphism Classes ◽  
Degree Pattern ◽  
A Finite Group

Let M be a finite group and D (M) be the degree pattern of M. Denote by h OD (M) the number of isomorphism classes of finite groups G with the same order and degree pattern as M. A finite group M is called k-fold OD-characterizable if h OD (M) = k. Usually, a 1-fold OD-characterizable group is simply called OD-characterizable. The purpose of this article is twofold. First, it provides some information on the structure of a group from its degree pattern. Second, it proves that the projective special linear groups L4(4), L4(8), L4(9), L4(11), L4(13), L4(16), L4(17) are OD-characterizable.

scholarly journals Projective representations of extra-special p-groups

1978 ◽  
Vol 19 (2) ◽  
pp. 149-152 ◽  
Author(s):  
Hans Opolka
Keyword(s):  
Finite Group ◽  
Characteristic Zero ◽  
Cohomology Group ◽  
Multiplicative Group ◽  
Neutral Element ◽  
Closed Field ◽  
Algebra Isomorphism ◽  
Twisted Group Algebra ◽  
Projective Representations ◽  
A Finite Group

Let G be a finite group (with neutral element e) which operates trivially on the multiplicative group R* of a commutative ring R (with identity 1). Let H2(G, R*) denote the second cohomology group of G with respect to the trivial G-module R*. With every represented by the central factor system we associate the so called twisted group algebra (R, G, f) (see [3, V, 23.7] for the definition). (R, G, f) is determined by f up to R-algebra isomorphism. In this note we shall describe its representations in the case R is an algebraically closed field C of characteristic zero and G is an extra-special p-group P.

scholarly journals On tensor factorisation for representations of finite groups

2004 ◽  
Vol 69 (1) ◽  
pp. 161-171 ◽  
Author(s):  
Emanuele Pacifici
Keyword(s):  
Finite Group ◽  
Tensor Product ◽  
Finite Groups ◽  
Group Structure ◽  
Complex Representation ◽  
Normal Subgroups ◽  
Representations Of Finite Groups ◽  
Projective Representations ◽  
A Finite Group

We prove that, given a quasi-primitive complex representation D for a finite group G, the possible ways of decomposing D as an inner tensor product of two projective representations of G are parametrised in terms of the group structure of G. More explicitly, we construct a bijection between the set of such decompositions and a particular interval in the lattice of normal subgroups of G.

Real projective representations of finite groups

1990 ◽  
Vol 107 (1) ◽  
pp. 27-32 ◽  
Author(s):  
P. N. Hoffmann ◽  
J. F. Humphreys
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Schur Multiplier ◽  
Representations Of Finite Groups ◽  
Projective Representations ◽  
A Finite Group

The projective representations of a finite group G over a field K are divided into sets, each parametrized by an element of the group H2(G, Kx). The latter is the Schur multiplier M(G) when K = ℂ.

scholarly journals Groups whose Projective character degrees are powers of a prime

1988 ◽  
Vol 30 (2) ◽  
pp. 177-180 ◽  
Author(s):  
R. J. Higgs
Keyword(s):  
Finite Group ◽  
Projective Representation ◽  
Character Degrees ◽  
Projective Character ◽  
Projective Representations ◽  
A Finite Group

Let Gbe a finite group, and P:G → GL(n, ) be such that for all x, y ∈ G(i) P(x)P(y) = α(x, y)P(xy), and(ii)P(l) = In,where α(x, y) ∈ *; then P is a projective representation of G with cocycle α and degree n. For other basic definitions concerning projective representations see [4].

scholarly journals The identity of certain representation algebra decompositions

1970 ◽  
Vol 3 (1) ◽  
pp. 73-74
Author(s):  
S. B. Conlon ◽  
W. D. Wallis
Keyword(s):  
Finite Group ◽  
Tensor Product ◽  
Linear Algebra ◽  
Residue Field ◽  
Complex Field ◽  
Direct Sums ◽  
Isomorphism Classes ◽  
Direct Sum ◽  
A Finite Group ◽  
Representation Algebra

Let G be a finite group and F a complete local noetherian commutative ring with residue field of characteristic p # 0. Let A(G) denote the representation algebra of G with respect to F. This is a linear algebra over the complex field whose basis elements are the isomorphism-classes of indecomposable finitely generated FG-representation modules, with addition and multiplication induced by direct sum and tensor product respectively. The two authors have separately found decompositions of A(G) as direct sums of subalgebras. In this note we show that the decompositions in one case have a common refinement given in the other's paper.

Appendix

1982 ◽  
Vol 92 (1) ◽  
pp. 73-78 ◽  
Author(s):  
N. Spaltenstein
Keyword(s):  
Finite Group ◽  
Isomorphism Classes ◽  
A Finite Group

The notations and the references are the same as in the article by Alvis and Lusztig (0).For a finite group H let H^ be the set of isomorphism classes of irreducible complex representations of H. Let |θ| denote the degree of θ∈H^

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