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.

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

Every finite group action on a compact 3-manifold preserves infinitely many hyperbolic spatial graphs

2014 ◽  
Vol 23 (06) ◽  
pp. 1450034 ◽  
Author(s):  
Toru Ikeda
Keyword(s):  
Finite Group ◽  
Group Action ◽  
Group Actions ◽  
Infinite Family ◽  
Finite Group Action ◽  
Finite Group Actions ◽  
Spatial Graph ◽  
Cell Decompositions ◽  
Spatial Graphs ◽  
Ideal Triangulations

We consider symmetries of spatial graphs in compact 3-manifolds described by smooth finite group actions. This paper provides a method for constructing an infinite family of hyperbolic spatial graphs with given symmetry by connecting spatial graph versions of hyperbolic tangles in 3-cells of polyhedral cell decompositions induced from triangulations of the 3-manifolds. This method is applicable also to the case of ideal triangulations.

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.

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.

SEMIALGEBRAS AND THEIR ALGEBRAS OF DIFFERENCES WITH PARTIAL GROUP ACTIONS ON THEM

2013 ◽  
Vol 06 (03) ◽  
pp. 1350038
Author(s):  
Ram Parkash Sharma ◽  
Anu
Keyword(s):  
Finite Group ◽  
Prime Ideal ◽  
Group Actions ◽  
Rocky Mountain ◽  
Prime Ideals ◽  
Central Idempotent ◽  
Group Rings ◽  
Partial Action ◽  
Partial Group ◽  
A Finite Group

Let A be a semialgebra defined in [R. P. Sharma, Anu and N. Singh, Partial group actions on semialgebras, Asian European J. Math.5(4) (2012), Article ID:1250060, 20pp.] over an additively cancellative and commutative semiring K. In additively cancellative semirings, the subtractive ideals play an important role. If P is a subtractive and G-prime ideal of an additively cancellative and yoked semiring A, where G is a finite group acting on A, then A has finitely many n(≤ |G|) minimal primes over P (see [R. P. Sharma and T. R. Sharma, G-prime ideals in semirings and their skew group rings, Comm. Algebra34 (2006) 4459–4465], Lemma 3.6, a result analogous to Lemma 3.2 of Passman [D. S. Passman, It's essentially Maschke's theorem, Rocky Mountain J. Math.13 (1983) 37–54]). Consider a subtractive partial action α of a finite group G on A such that each Dg is generated by a central idempotent 1g of A and the intersection D = ⋂g∈G,Dg≠0Dg of nonzero Dg's is nonzero. It is not necessary that number of minimal primes in Spec A over a subtractive and α-prime ideal P of a yoked semiring A is less than or equal to the order of the group, if 1d ∈ P (Example 3.2). However, we show that the result is true if 1d ∉ P (Corollary 3.1). We also study the prime ideals of the partial fixed subsemiring Aα of A.

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