Černý’s conjecture and group representation theory
نویسندگان
چکیده
منابع مشابه
Černý’s conjecture and group representation theory
Let us say that a Cayley graph of a group G of order n is a Černý Cayley graph if every synchronizing automaton containing as a subgraph with the same vertex set admits a synchronizing word of length at most (n− 1)2. In this paper we use the representation theory of groups over the rational numbers to obtain a number of new infinite families of Černý Cayley graphs.
متن کاملRepresentation Theory, Topological Field Theory, and the Andrews-curtis Conjecture
We pose a representation-theoretic question motivated by an attempt to resolve the Andrews-Curtis conjecture. Roughly, is there a triangular Hopf algebra with a collection of self-dual irreducible representations Vi so that the product of any two decomposes as a sum of copies of the Vi, and ∑ (rank Vi) 2 = 0? This data can be used to construct a “topological quantum field theory” on 2complexes ...
متن کاملGroup representation theory and quantum physics∗
This is a basic tutorial on the use of group representation theory in quantum physics, in particular for such systems as molecules and crystals, which forms the basis of spectroscopic studies in physics and chemistry. Note that, despite the now venerable character of the aforementioned scientific endeavors, group representation theory still finds interesting and novel applications, such as the ...
متن کاملVoting, the Symmetric Group, and Representation Theory
We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied QSn-modules. By using only a handful of simple combinatorial objects (e.g., tabloids) and some basic ideas from representation theory (e.g., Schur's Lemma), this allows us to recast and extend some well-known results in the field of voting theory.
متن کاملThe Auslander-Reiten Conjecture for Group Rings
This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2009
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-009-0185-0