1,349 research outputs found
Invariance of KMS states on graph C*-algebras under classical and quantum symmetry
We study invariance of KMS states on graph C*-algebras coming from strongly
connected and circulant graphs under the classical and quantum symmetry of the
graphs. We show that the unique KMS state for strongly connected graphs is
invariant under quantum automorphism group of the graph. For circulant graphs,
it is shown that the action of classical and quantum automorphism group
preserves only one of the KMS states occurring at the critical inverse
temperature. We also give an example of a graph C*-algebra having more than one
KMS state such that all of them are invariant under the action of classical
automorphism group of the graph, but there is a unique KMS state which is
invariant under the action of quantum automorphism group of the graph.Comment: 15 pages, 2 figure
Hopf coactions on commutative algebras generated by a quadratically independent comodule
Let A be a commutative unital algebra over an algebraically closed field k of
characteristic not equal to 2, whose generators form a finite-dimensional
subspace V, with no nontrivial homogeneous quadratic relations. Let Q be a Hopf
algebra that coacts on A inner-faithfully, while leaving V invariant. We prove
that Q must be commutative when either: (i) the coaction preserves a
non-degenerate bilinear form on V; or (ii) Q is co-semisimple,
finite-dimensional, and char(k)=0.Comment: v2: 4 pages. To appear in Communications in Algebr
Classification of Cayley Rose Window Graphs
Rose window graphs are a family of tetravalent graphs, introduced by Steve Wilson. Following it, Kovacs, Kutnar and Marusic classified the edge-transitive rose window graphs and Dobson, Kovacs and Miklavic characterized the vertex transitive rose window graphs. In this paper, we classify the Cayley rose window graphs
On Some Intersection Properties of Finite Groups
In this article, we introduce the study of a class of finite groups which
admits a subgroup which intersects all non-trivial subgroups of . We also
explore a subclass of it consisting of all groups in which the prime order
elements commute. In particular, we discuss the relationship between these
class of groups with other known classes of finite groups, like simple groups,
perfect groups etc. Moreover, we also prove some results on the possible orders
of such groups. Finally, we conclude with some open issues.Comment: 12 pages, 1 figur
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