Relationships between generalized Heisenberg algebras and the classical Heisenberg algebra

• Autorzy: Marc Fabbri , Frank Okoh
• Języki publikacji: EN

Abstrakty

EN

A Lie algebra is called a generalized Heisenberg algebra of degree n if its centre coincides with its derived algebra and is n-dimensional. In this paper we define for each positive integer n a generalized Heisenberg algebra 𝓗ₙ. We show that 𝓗ₙ and 𝓗 ₁ⁿ, the Lie algebra which is the direct product of n copies of 𝓗 ₁, contain isomorphic copies of each other. We show that 𝓗ₙ is an indecomposable Lie algebra. We prove that 𝓗ₙ and 𝓗 ₁ⁿ are not quotients of each other when n ≥ 2, but 𝓗 ₁ is a quotient of 𝓗ₙ for each positive integer n. These results are used to obtain several families of 𝓗ₙ-modules from the Fock space representation of 𝓗 ₁. Analogues of Verma modules for 𝓗ₙ, n ≥ 2, are also constructed using the set of rational primes.

Kategorie tematyczne

• 17B65: Infinite-dimensional Lie (super)algebras
• 17B69: Vertex operators; vertex operator algebras and related structures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 134
• Numer: 2
• Strony: 255-265

Daty

wydano

2014

Twórcy

autor

Marc Fabbri

• Department of Mathematics, Pennsylvania State University, University Park, PA 16802-6401, U.S.A.

autor

Frank Okoh

• Department of Mathematics, Wayne State University, Detroit, MI 48202-3622, U.S.A.

Identyfikatory

DOI

10.4064/cm134-2-9