Derivation Algebra in Noncommutative Group Algebras

2020 ◽  
Vol 308 (1) ◽  
pp. 22-34
Author(s):  
A. A. Arutyunov
Keyword(s):  
Group Algebras ◽  
Derivation Algebra

Complex group algebras of the direct product of non-isomorphic Suzuki groups

2019 ◽  
Vol 19 (02) ◽  
pp. 2050036
Author(s):  
Morteza Baniasad Azad ◽  
Behrooz Khosravi
Keyword(s):  
Direct Product ◽  
Group Algebra ◽  
Irreducible Character ◽  
Prime Numbers ◽  
Product Formula ◽  
Character Degrees ◽  
Group Algebras ◽  
Complex Group ◽  
Complex Group Algebra ◽  
Suzuki Groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

Group Algebras with Locally Nilpotent Unit Groups

2015 ◽  
Vol 44 (2) ◽  
pp. 604-612 ◽  
Author(s):  
M. Ramezan-Nassab
Keyword(s):  
Group Algebras ◽  
Locally Nilpotent

scholarly journals Free group algebras in Malcev–Neumann skew fields of fractions

2014 ◽  
Vol 26 (2) ◽  
Author(s):  
Javier Sánchez
Keyword(s):  
Free Group ◽  
Group Algebras ◽  
Skew Fields

AbstractLet

On *-clean non-commutative group rings

2016 ◽  
Vol 15 (08) ◽  
pp. 1650150 ◽  
Author(s):  
Hongdi Huang ◽  
Yuanlin Li ◽  
Gaohua Tang
Keyword(s):  
Finite Field ◽  
Local Ring ◽  
Group Algebra ◽  
Rational Numbers ◽  
Semisimple Group ◽  
Group Algebras ◽  
Group Rings ◽  
Dihedral Groups ◽  
Commutative Local Ring ◽  
Generalized Quaternion

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups [Formula: see text], and the generalized quaternion groups [Formula: see text] with standard involution ∗. For the non-semisimple group algebra case, we characterize the ∗-cleanness of [Formula: see text] with a prime [Formula: see text], and [Formula: see text] with [Formula: see text], where [Formula: see text] is a commutative local ring. For the semisimple group algebra case, we investigate when [Formula: see text] is ∗-clean, where [Formula: see text] is the field of rational numbers [Formula: see text] or a finite field [Formula: see text] and [Formula: see text] or [Formula: see text].

Primitive group algebras of polycyclic groups

1978 ◽  
Vol 19 (1) ◽  
pp. 25-30 ◽  
Author(s):  
O. I. Domanov
Keyword(s):  
Primitive Group ◽  
Group Algebras ◽  
Polycyclic Groups

Semisimple metacyclic group algebras

2011 ◽  
Vol 121 (4) ◽  
pp. 379-396 ◽  
Author(s):  
GURMEET K BAKSHI ◽  
SHALINI GUPTA ◽  
INDER BIR S PASSI
Keyword(s):  
Group Algebras ◽  
Metacyclic Group

scholarly journals Solutions of the Yang–Baxter equation: Descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

2011 ◽  
Vol 847 (2) ◽  
pp. 387-412 ◽  
Author(s):  
P.E. Finch ◽  
K.A. Dancer ◽  
P.S. Isaac ◽  
J. Links
Keyword(s):  
Dihedral Group ◽  
Group Algebras ◽  
Baxter Equation ◽  
Vertex Model
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