منابع مشابه
Representations of the Renner Monoid
We describe irreducible representations and character formulas of the Renner monoids for reductive monoids, which generalizes the Munn-Solomon representation theory of rook monoids to any Renner monoids. The type map and polytope associated with reductive monoids play a crucial role in our work. It turns out that the irreducible representations of certain parabolic subgroups of the Weyl groups ...
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Let n be a positive integer and let n = {1, . . . , n}. Let R be the set of all oneto-one maps σ with domain I (σ ) ⊆ n and range J (σ) ⊆ n. If i ∈ I (σ ) let iσ denote the image of i under σ . There is an associative product (σ, τ ) → στ on R defined by composition of maps: i(στ)= (iσ )τ if i ∈ I (σ ) and iσ ∈ I (τ ). Thus the domain I (στ) consists of all i ∈ I (σ ) such that iσ ∈ I (τ ). The...
متن کاملThe monoid of families of quiver representations
The aim of this paper is to develop an algebraic tool, namely the monoid structure on families of quiver representations as stated in the title, which is directly related both to quantized Kac-Moody algebras, and to geometric properties of varieties of representations. Although this new structure is far from being understood in detail, it it easily accessible to explicit calculations, and it pr...
متن کاملThe Ring of Regular Functions of an Algebraic Monoid Lex Renner and Alvaro Rittatore
Let M be an irreducible normal algebraic monoid with unit group G. It is known that G admits a Rosenlicht decomposition, G = GantGaff ∼= (Gant × Gaff)/Gaff ∩ Gant, where Gant is the maximal anti-affine subgroup of G, and Gaff the maximal normal connected affine subgroup of G. In this paper we show that this decomposition extends to a decomposition M = GantMaff ∼= Gant∗Gaff∩GantMaff , where Maff...
متن کاملRepresentations through a monoid on the set of fuzzy implications
Fuzzy implications are one of the most important fuzzy logic connectives. In this work, we conduct a systematic algebraic study on the set I of all fuzzy implications. To this end, we propose a binary operation, denoted by ~, which makes (I,~) a non-idempotent monoid. While this operation does not give a group structure, we determine the largest subgroup S of this monoid and using their represe...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2009
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196709005147