Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: It is proved that for every bipartite graph G, its list-homomorphism problem is tractable if and only if G admits a monochromatic conservative semilattice operation and can easily be solved by a combination of two-colouring and arc-consistency.
5 citations
TL;DR: This paper identifies in which of these upper-bound semirings in tropical algebra the authors can express symmetric polynomials in terms of elementary ones and shows that in the case of idempotentSemirings this is always possible, and that in non-trivial symmetrized semiring this is never possible.
5 citations
20 Feb 2017
TL;DR: In this article, natural quantum versions of idempotence and distributivity are specified for quantum quasigroups and loops, which furnish solutions to the quantum Yang-Baxter equation.
Abstract: Quantum quasigroups and loops are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.
5 citations
TL;DR: In this article, it was shown that a certain idempotent truncation of a RoCK block of weight d of a symmetric group defined over a field F of characteristic e is Morita equivalent to the principal block of the wreath product.
Abstract: We consider RoCK (or Rouquier) blocks of symmetric groups and Hecke algebras at roots of unity. We prove a conjecture of Turner asserting that a certain idempotent truncation of a RoCK block of weight d of a symmetric group $${\mathfrak {S}}_n$$
defined over a field F of characteristic e is Morita equivalent to the principal block of the wreath product $$\mathfrak S_e \wr \mathfrak S_d$$
. This generalises a theorem of Chuang and Kessar that applies to RoCK blocks with abelian defect groups. Our proof relies crucially on an isomorphism between $$F{\mathfrak {S}}_n$$
and a cyclotomic Khovanov–Lauda–Rouquier algebra, and the Morita equivalence we produce is that of graded algebras. We also prove the analogous result for an Iwahori–Hecke algebra at a root of unity defined over an arbitrary field.
5 citations
TL;DR: In this paper, the authors apply a result of Herstein to simple C*-algebras which arise as quotients of properly infinite von Neumann algebrains.
5 citations