QUASITRIANGULAR HOPF ALGEBRAS OF DIMENSION pq

2002 ◽  
Vol 34 (3) ◽  
pp. 301-307 ◽  
Author(s):  
SONIA NATALE
Keyword(s):  
Group Algebra ◽  
Hopf Algebras ◽  
Characteristic Zero ◽  
Prime Numbers ◽  
Closed Field ◽  
Algebraically Closed Field

Let p and q be odd prime numbers. It is shown that all quasitriangular Hopf algebras of dimension pq over an algebraically closed field k of characteristic zero are semisimple and therefore isomorphic to a group algebra.

HOPF ALGEBRAS OF DIMENSION 30

2010 ◽  
Vol 09 (01) ◽  
pp. 11-15 ◽  
Author(s):  
DAIJIRO FUKUDA
Keyword(s):  
Hopf Algebra ◽  
Group Algebra ◽  
Hopf Algebras ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Finite Dimensional

This paper contributes to the classification of finite dimensional Hopf algebras. It is shown that every Hopf algebra of dimension 30 over an algebraically closed field of characteristic zero is semisimple and thus isomorphic to a group algebra or the dual of a group algebra.

On Semisimple Hopf Algebras of Dimension pqn

2014 ◽  
Vol 57 (2) ◽  
pp. 264-269
Author(s):  
Li Dai ◽  
Jingcheng Dong
Keyword(s):  
Hopf Algebra ◽  
Group Algebra ◽  
Hopf Algebras ◽  
Prime Numbers ◽  
Closed Field ◽  
Semisimple Hopf Algebra ◽  
Algebraically Closed Field

AbstractLet p, q be prime numbers with p2 < q, n ∊ ℕ, and H a semisimple Hopf algebra of dimension pqn over an algebraically closed field of characteristic 0. This paper proves that H must possess one of the following two structures: (1) H is semisolvable; (2) H is a Radford biproduct R#kG, where kG is the group algebra of group G of order p and R is a semisimple Yetter–Drinfeld Hopf algebra in of dimension qn.

On the classification of finite quasi-quantum groups

2017 ◽  
Vol 29 (10) ◽  
pp. 1730003 ◽  
Author(s):  
Mamta Balodi ◽  
Hua-Lin Huang ◽  
Shiv Datt Kumar
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Tools And Methods

We give an overview of the classification results obtained so far for finite quasi-quantum groups over an algebraically closed field of characteristic zero. The main classification results on basic quasi-Hopf algebras are obtained by Etingof, Gelaki, Nikshych, and Ostrik, and on dual quasi-Hopf algebras by Huang, Liu and Ye. The objective of this survey is to help in understanding the tools and methods used for the classification.

Traceless tensors and invariants

1998 ◽  
Vol 124 (1) ◽  
pp. 73-80 ◽  
Author(s):  
MIHALIS MALIAKAS
Keyword(s):  
Symmetric Group ◽  
Group Algebra ◽  
Characteristic Zero ◽  
Orthogonal Group ◽  
Classical Group ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Special Orthogonal Group ◽  
Related Characteristic ◽  
Centralizer Algebra

For G a classical group of type Bn, Cn or Dn defined over an algebraically closed field (of characteristic other than two if G is a special orthogonal group), we show that the centralizer algebra of G on the space of endomorphisms of the module of traceless tensors Wr is naturally isomorphic to the group algebra of the symmetric group Sr if r[les ]n (for G of type Bn or Cn) or if r<n (for G of type Dn). This extends a characteristic zero result of Brauer and Weyl and recovers some of the related characteristic free results that De Concini and Strickland obtained for G of type Cn.

scholarly journals NON-AFFINE HOPF ALGEBRA DOMAINS OF GELFAND–KIRILLOV DIMENSION TWO

2017 ◽  
Vol 59 (3) ◽  
pp. 563-593
Author(s):  
K. R. GOODEARL ◽  
J. J. ZHANG
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Characteristic Zero ◽  
Closed Field ◽  
Integral Domains ◽  
Algebraically Closed Field ◽  
Kirillov Dimension

AbstractWe classify all non-affine Hopf algebras H over an algebraically closed field k of characteristic zero that are integral domains of Gelfand–Kirillov dimension two and satisfy the condition Ext1H(k, k) ≠ 0. The affine ones were classified by the authors in 2010 (Goodearl and Zhang, J. Algebra324 (2010), 3131–3168).

H-Simple module algebras for eight-dimensional non-semisimple Hopf algebras

2016 ◽  
Vol 15 (07) ◽  
pp. 1650134
Author(s):  
Fengxia Gao ◽  
Shilin Yang
Keyword(s):  
Hopf Algebras ◽  
Characteristic Zero ◽  
Jacobson Radical ◽  
Simple Module ◽  
Simple Algebra ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Finite Dimensional ◽  
Module Algebras

Let [Formula: see text] be an algebraically closed field of characteristic zero. For all eight-dimensional non-semisimple Hopf algebras [Formula: see text] which are either pointed or unimodular, we characterrize all finite-dimensional [Formula: see text]-simple module algebras. As a bonus of our approach, it is shown that for any [Formula: see text]-simple algebra, the nilpotent index of the Jacobson radical is at most three.

scholarly journals An algebraically closed field

1968 ◽  
Vol 9 (2) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Rayner
Keyword(s):  
Positive Integer ◽  
Power Series ◽  
Formal Power Series ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Zero Characteristic ◽  
Image Position ◽  
Formal Power ◽  
Puiseux Expansions

Letkbe any algebraically closed field, and denote byk((t)) the field of formal power series in one indeterminatetoverk. Letso thatKis the field of Puiseux expansions with coefficients ink(each element ofKis a formal power series intl/rfor some positive integerr). It is well-known thatKis algebraically closed if and only ifkis of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous toKwhich is algebraically closed whenkhas non-zero characteristicp. In this paper, I prove that the setLof all formal power series of the form Σaitei(where (ei) is well-ordered,ei=mi|nprt,n∈ Ζ,mi∈ Ζ,ai∈k,ri∈ Ν) forms an algebraically closed field.

scholarly journals Fibrations with moving cuspidal singularities

1991 ◽  
Vol 122 ◽  
pp. 161-179 ◽  
Author(s):  
Yoshifumi Takeda
Keyword(s):  
Algebraic Geometry ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Closed Field ◽  
Projective Surface ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Algebraically Closed Field ◽  
Smooth Projective Surface ◽  
Almost All

Let f: V → C be a fibration from a smooth projective surface onto a smooth projective curve over an algebraically closed field k. In the case of characteristic zero, almost all fibres of f are nonsingular. In the case of positive characteristic, it is, however, known that there exist fibrations whose general fibres have singularities. Moreover, it seems that such fibrations often have pathological phenomena of algebraic geometry in positive characteristic (see M. Raynaud [7], W. Lang [4]).

Abelian Gradings on Upper Block Triangular Matrices

2012 ◽  
Vol 55 (1) ◽  
pp. 208-213 ◽  
Author(s):  
Angela Valenti ◽  
Mikhail Zaicev
Keyword(s):  
Abelian Group ◽  
Characteristic Zero ◽  
Finite Abelian Group ◽  
Triangular Matrix ◽  
Closed Field ◽  
Triangular Matrices ◽  
Algebraically Closed Field ◽  
Matrix Algebras ◽  
Block Triangular Matrix

AbstractLet G be an arbitrary finite abelian group. We describe all possible G-gradings on upper block triangular matrix algebras over an algebraically closed field of characteristic zero.

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