2021
DOI: 10.48550/arxiv.2110.04469
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The $n$-dimensional quadratic Heisenberg algebra as a "non--commutative" $\rm{sl}(2,\mathbb{C})$

Luigi Accardi,
Andreas Boukas,
Yun-Gang Lu

Abstract: We prove that the commutation relations among the generators of the quadratic Heisenberg algebra of dimension n ∈ N, look like a kind of non-commutative extension of sl(2, C) (more precisely of its unique 1dimensional central extension), denoted heis 2;C (n) and called the complex n-dimensional quadratic Boson algebra. This non-commutativity has a different nature from the one considered in quantum groups. We prove the exponentiability of these algebras (for any n) in the Fock representation. We obtain the gro… Show more

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