scholarly journals Normal forms of invariant vector fields under a finite group action

1993 ◽  
Vol 37 ◽  
pp. 75-82
Author(s):  
F. Sánchez-Bringas
Keyword(s):  
Finite Group ◽  
Group Action ◽  
Vector Fields ◽  
Normal Forms ◽  
Finite Group Action ◽  
Invariant Vector ◽  
A Finite Group ◽  
Invariant Vector Fields

Reflection Subquotients of Unitary Reflection Groups

1999 ◽  
Vol 51 (6) ◽  
pp. 1175-1193 ◽  
Author(s):  
G. I. Lehrer ◽  
T. A. Springer
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Vector Fields ◽  
Reflection Group ◽  
Complex Vector Space ◽  
Reflection Groups ◽  
Complex Vector ◽  
Invariant Vector ◽  
A Finite Group ◽  
Invariant Vector Fields

AbstractLet G be a finite group generated by (pseudo-) reflections in a complex vector space and let g be any linear transformation which normalises G. In an earlier paper, the authors showed how to associate with any maximal eigenspace of an element of the coset gG, a subquotient of G which acts as a reflection group on the eigenspace. In this work, we address the questions of irreducibility and the coexponents of this subquotient, as well as centralisers in G of certain elements of the coset. A criterion is also given in terms of the invariant degrees of G for an integer to be regular for G. A key tool is the investigation of extensions of invariant vector fields on the eigenspace, which leads to some results and questions concerning the geometry of intersections of invariant hypersurfaces.

On the Equivariant Formality of Kähler Manifolds With Finite Group Action

1993 ◽  
Vol 45 (6) ◽  
pp. 1200-1210 ◽  
Author(s):  
Benjamin L. Fine ◽  
Georgia Triantafillou
Keyword(s):  
Finite Group ◽  
Group Action ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Maps ◽  
Finite Group Action ◽  
Equivariant Maps ◽  
Definition Of ◽  
A Finite Group

AbstractAn appropriate definition of equivariant formality for spaces equipped with the action of a finite group G, and for equivariant maps between such spaces, is given. Kahler manifolds with holomorphic G-actions, and equivariant holomorphic maps between such Kàhler manifolds, are proven to be equivariantly formal, generalizing results of Deligne, Griffiths, Morgan, and Sullivan

CLASSES MINIMALES DE RÉSEAUX ET RÉTRACTIONS GÉOMÉTRIQUES ÉQUIVARIANTES DANS LES ESPACES SYMÉTRIQUES

2001 ◽  
Vol 64 (2) ◽  
pp. 275-286 ◽  
Author(s):  
CHRISTOPHE BAVARD
Keyword(s):  
Finite Group ◽  
Euclidean Space ◽  
Symmetric Space ◽  
Group Action ◽  
Symmetric Spaces ◽  
Classification Problem ◽  
Finite Group Action ◽  
Natural Geometry ◽  
A Finite Group

Equivariant and cocompact retractions of certain symmetric spaces are constructed. These retractions are defined using the natural geometry of symmetric spaces and in relation to the theory of lattices of euclidean space. The following cases are considered: the symmetric space corresponding to lattices endowed with a finite group action, from which is obtained some information relating to the classification problem of these lattices, and the Siegel space Sp2g(R)/Ug, for which a natural Sp2g(Z)-equivariant cocompact retract of codimension 1 is obtained.

scholarly journals Equivariant K-stability under finite group action

2021 ◽  
Author(s):  
Yuchen Liu ◽  
Ziwen Zhu
Keyword(s):  
Finite Group ◽  
Group Action ◽  
Finite Group Action ◽  
A Finite Group

We show that [Formula: see text]-equivariant K-semistability (respectively, [Formula: see text]-equivariant K-polystability) implies K-semistability (respectively, K-polystability) for log Fano pairs with klt singularities when [Formula: see text] is a finite group.

Group Actions on Quasi-Baer Rings

2009 ◽  
Vol 52 (4) ◽  
pp. 564-582 ◽  
Author(s):  
Hai Lan Jin ◽  
Jaekyung Doh ◽  
Jae Keol Park
Keyword(s):  
Finite Group ◽  
Group Action ◽  
Semiprime Ring ◽  
Group Actions ◽  
Group Rings ◽  
Finite Group Action ◽  
Baer Rings ◽  
Skew Group Rings ◽  
A Finite Group ◽  
The Right

AbstractA ring R is called quasi-Baer if the right annihilator of every right ideal of R is generated by an idempotent as a right ideal. We investigate the quasi-Baer property of skew group rings and fixed rings under a finite group action on a semiprime ring and their applications to C*-algebras. Various examples to illustrate and delimit our results are provided.

A Combinatorial Determinant Dual to the Group Determinant

2015 ◽  
Vol 29 ◽  
pp. 17-29
Author(s):  
Murali Srinivasan ◽  
Ashish Mishra
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Group Action ◽  
Dimensional Vector ◽  
Finite Group Action ◽  
Irreducible Polynomials ◽  
Dimensional Vector Space ◽  
Finite Set ◽  
A Finite Group

We define the commuting algebra determinant of a finite group action on a finite set, a notion dual to the group determinant of Dedekind. We give the following combinatorial example of a commuting algebra determinant. Let $\Bq(n)$ denote the set of all subspaces of an $n$-dimensional vector space over $\Fq$. The {\em type} of an ordered pair $(U,V)$ of subspaces, where $U,V\in \Bq(n)$, is the ordered triple $(\mbox{dim }U, \mbox{dim }V, \mbox{dim }U\cap V)$ of nonnegative integers. Assume that there are independent indeterminates corresponding to each type. Let $X_q(n)$ be the $\Bq(n)\times \Bq(n)$ matrix whose entry in row $U$, column $V$ is the indeterminate corresponding to the type of $(U,V)$. We factorize the determinant of $X_q(n)$ into irreducible polynomials.

Sign in / Sign up

Export Citation Format

Share Document