Transitive maps from posets to Dynkin diagrams
- Misra, Kailash C.
- Putcha, Mohan S.
- Singh, Daya S.
Publication date
March 1990
DOI Publisher
Published by Elsevier B.V. ISSN
0022-4049Abstract
AbstractLet G be a group with a BN-pair and Γ its Dynkin diagram. Let P be a partially ordered set and λ:P→2Γ be a map from P into the induced subgraphs of Γ. We say that the map λ is transitive if for any a,b,c∈P with a<b<c, each component of λ(b) is contained in either λ(a) or λ(c). Transitive maps characterize the systems of idempotents of certain monoids having G as the group of units. In this paper we construct a universal transitive map, which is then used to describe all transitive maps
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