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Basic Properties of Generalized Down–up Algebras by Thomas Cassidy; Brad Shelton is a Mathematics article available to read on EtoBox.
What is Basic Properties of Generalized Down–up Algebras about?
We introduce a large class of infinite dimensional associative algebras which generalize down-up algebras. Let K be a field and fix f ∈ K[x] and r, s, γ ∈ K. Define L = L(f, r, s, γ ) to be the algebra generated by d, u and h with defining relations: Included in this family are Smith's class of algebras similar to U(sl 2 ), Le Bruyn's conformal sl 2 enveloping algebras and the algebras studied by Rueda. The algebras L have Gelfand-Kirillov dimension 3 and are Noetherian domains if and only if rs = 0. We calculate the global dimension of L and, for rs = 0, classify the simple weight modules for L, including all finite dimensional simple modules. Simple weight modules need not be classical highest weight modules.
Who reads Basic Properties of Generalized Down–up Algebras?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Thomas Cassidy; Brad Shelton
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0021-8693)
- Published
- 2004
- Language
- EN
- Field
- Mathematics (Physical Sciences)