The Center of a Regular Algebraic Monoid

1999 ◽  
Vol 59 (3) ◽  
pp. 334-341 ◽  
Author(s):  
Yu Chen ◽  
Wenxue Huang
Keyword(s):  
Algebraic Monoid

CARTAN SUBMONOIDS OF ALGEBRAIC MONOIDS

1995 ◽  
Vol 05 (03) ◽  
pp. 367-377 ◽  
Author(s):  
WENXUE HUANG
Keyword(s):  
Maximal Torus ◽  
Unit Group ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Completely Regular ◽  
Algebraic Monoid ◽  
Algebraic Monoids

Let M be an irreducible linear algebraic monoid defined over an algebraically closed field K with idempotent set E(M), T a maximal torus of the unit group G of M. We call CM(T)c a Cartan submonoid of M. The following are proved: (1) If M is reductive with zero or completely regular, then CM(T) is irreducible and regular and [Formula: see text]; (2) If M is regular, then M is solvable iff NM(CM(T))=CM(T), in which case, CM(T) is irreducible and regular; (3) If M is regular, then [Formula: see text].

Conjugacy Classes in Algebraic Monoids II

1994 ◽  
Vol 46 (3) ◽  
pp. 648-661 ◽  
Author(s):  
Mohan S. Putcha
Keyword(s):  
Unit Group ◽  
Conjugacy Classes ◽  
Reductive Groups ◽  
Bijective Correspondence ◽  
Twisted Conjugacy ◽  
Algebraic Monoid ◽  
Algebraic Monoids

AbstractLet M be a connected linear algebraic monoid with zero and a reductive unit group. We show that there exist reductive groups G1,..., Gt, each with an automorphism, such that the conjugacy classes of M are in a natural bijective correspondence with the twisted conjugacy classes of Gi, i = 1,..., t.

THE BRAID ROOK MONOID

2008 ◽  
Vol 18 (04) ◽  
pp. 779-802 ◽  
Author(s):  
EDDY GODELLE
Keyword(s):  
Group Theory ◽  
Coxeter Group ◽  
Coxeter Groups ◽  
Hecke Algebra ◽  
Linear Algebraic Group ◽  
Weyl Groups ◽  
Rook Monoid ◽  
Algebraic Monoid ◽  
Tits Group

In linear algebraic monoid theory, the Renner monoids play the role of the Weyl groups in linear algebraic group theory. It is well known that Weyl groups are Coxeter groups, and that we can associate a Hecke algebra and an Artin–Tits group to each Coxeter group. The question of the existence of a Hecke algebra associated with each Renner monoid has been positively answered. In this paper we discuss the question of the existence of an equivalent of the Artin–Tits groups in the framework of Renner monoids. We consider the seminal case of the rook monoid and introduce a new length function.

Affinely spanned quasi-stochastic algebraic monoids

2017 ◽  
Vol 27 (08) ◽  
pp. 1061-1072
Author(s):  
W. Huang ◽  
J. Li
Keyword(s):  
Matrix Element ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Unit Group ◽  
Initial Study ◽  
Zariski Closure ◽  
Closed Field ◽  
Basic Class ◽  
Algebraic Monoid ◽  
Algebraic Monoids

A linear algebraic monoid over an algebraically closed field [Formula: see text] of characteristic zero is called (row) quasi-stochastic if each row of each matrix element is of sum one. Any linear algebraic monoid over [Formula: see text] can be embedded as an algebraic submonoid of the maximum affinely spanned quasi-stochastic monoid of some degree [Formula: see text]. The affinely spanned quasi-stochastic algebraic monoids form a basic class of quasi-stochastic algebraic monoids. An initial study of structure of affinely spanned quasi-stochastic algebraic monoids is conducted. Among other things, it is proved that the Zariski closure of a parabolic subgroup of the unit group of an affinely spanned quasi-stochastic algebraic monoid is affinely spanned.

scholarly journals Products of idempotents in algebraic monoids

2006 ◽  
Vol 80 (2) ◽  
pp. 193-203 ◽  
Author(s):  
Mohan S. Putcha
Keyword(s):  
Sufficient Conditions ◽  
Unit Group ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Monoid ◽  
Necessary And Sufficient ◽  
Algebraic Monoids

AbstractLet M be a reductive algebraic monoid with zero and unit group G. We obtain a description of the submonoid generated by the idempotents of M. In particular, we find necessary and sufficient conditions for M\G to be idempotent generated.

scholarly journals The Centraliser of a Semisimple Element on a Reductive Algebraic Monoid

1999 ◽  
Vol 218 (1) ◽  
pp. 117-125 ◽  
Author(s):  
M.Eileen Hull ◽  
Lex E. Renner
Keyword(s):  
Semisimple Element ◽  
Algebraic Monoid

AN ALGEBRAIC MONOID APPROACH TO LINEAR ASSOCIATIVE ALGEBRAS, II

1996 ◽  
Vol 06 (05) ◽  
pp. 623-634 ◽  
Author(s):  
WENXUE HUANG
Keyword(s):  
Lie Algebra ◽  
Jacobson Radical ◽  
Borel Subgroup ◽  
Unit Group ◽  
Zariski Closure ◽  
Closed Field ◽  
Associative Algebras ◽  
Lie Bracket ◽  
Algebraic Monoid ◽  
Relationship Of

Let A be a linear associative K-algebra with unity (LAA), K an algebraically closed field. A K–subalgebra of A containing the unity of A is referred to as a sub-LAA of A. A with respect to the multiplication (respectively, Lie bracket) is an algebraic monoid (respectively, Lie algebra) over K, denoted by AM (respectively, AL). Let G(A) and J(A) denote the unit group of AM and Jacobson radical of A, respectively. The following are proved in this paper. (i) If BM is a Borel submonoid of AM, the Zariski closure of a Borel subgroup of G(A), then B is a sub-LAA of A and [Formula: see text], where [Formula: see text] is the set of Borel submonoids of AM. (ii) If dim A≠3, then G(A) is nilpotent iff for every proper sub-LAA N of A, G(N) is nilpotent. In addition, a relationship of Borel submonoids of AM and Borel subalgebras of AL is revealed.

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