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Down–Up Algebras and Their Representations

✍ Scribed by Rajesh S. Kulkarni

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 212 KB
Volume: 245
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8892

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A class of algebras called down-up algebras was introduced by G. Benkart and T. Roby (1998, J. Algebra 209, 305-344). We classify the finite dimensional simple modules over Noetherian down-up algebras and show that in some cases every finite dimensional module is semisimple. We also study the questi

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The algebra generated by the down and up operators on a differential or Ž . uniform partially ordered set poset encodes essential enumerative and structural properties of the poset. Motivated by the algebras generated by the down and up operators on posets, we introduce here a family of infinite-dim

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✍ Kaiming Zhao 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 144 KB

Down᎐up algebras which originated in the study of differential posets were recently defined and studied by Benkart and Roby. Benkart posed an open problem in her paper: to determine the centers of all down᎐up algebras. Here in this paper we completely solve this problem. As an application we also ge

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lie in a certain class of iterated skew polynomial rings, called ambiskew polynomial rings, in two indeterminates x and y over a commutative ring B. In such rings, commutation of the indeterminates with elements of B involve the same endomorphism σ of B, but from different sides, that is, yb = σ b y

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The partial group algebra of a group G over a field K, denoted by K G , is par the algebra whose representations correspond to the partial representations of G over K-vector spaces. In this paper we study the structure of the partial group Ž . algebra K G , where G is a finite group. In particular,

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