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Relationships between generalized Heisenberg algebras and the classical Heisenberg algebra

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Fabbri M., Okoh F.

Colloquium Mathematicum

2014

tom 134

nr 2

255-265

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fabbri M.

1 Okoh F.

1 2014

Wyniki wyszukiwania

Relationships between generalized Heisenberg algebras and the classical Heisenberg algebra