Results 131 to 140 of about 312 (162)

HEISENBERG–WEYL LIE ALGEBRA AND NATURAL EXPONENTIAL FAMILIES

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2007
We present in this work a specific construction of raising and lowering operators for 2-orthogonal quasi-monomial polynomials associated with continuous and discrete natural exponential families. We use these operators in order to characterize the real class of cubic natural exponential families.
openaire   +2 more sources

Associating quantum vertex algebras to deformed Heisenberg Lie algebras

Frontiers of Mathematics in China, 2011
In the paper under review, the author studies two deformed Heisenberg Lie algebras, denoted by \(H_q\) and \(\widetilde{H_q}\), and associates (quantum) vertex algebras to these Lie algebras. In both cases, a generating function associated to generators of the Lie algebra does not form a local set. In the first case, the generating function satisfies a
openaire   +2 more sources

The Betti numbers for Heisenberg Lie algebras

Journal of Algebraic Combinatorics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Higher Heisenberg Lie algebras and metaplectic representations

Journal für die reine und angewandte Mathematik (Crelles Journal), 1999
The existence of the Weil representation of the symplectic groups and of restrictions to dual reductive pairs is a most remarkable phenomenon. In this paper the author investigates its origins at the level of Lie algebras (over an arbitrary field of characteristic \(0\)). Let \(V\) be a finite-dimensional vector space over the field and let h\((n)\) be
openaire   +2 more sources

A very proper Heisenberg–Lie Banach *-algebra

Positivity, 2011
For each pair of non-zero real numbers q1 and q2, Laustsen and Silvestrov have constructed a unital Banach *-algebra \({\fancyscript{C}_{q_1,q_2}}\) which contains a universal normalized solution to the *-algebraic (q1, q2)-deformed Heisenberg–Lie commutation relations. We show that for (q1, q2) = (−1, 1), this Banach *-algebra is very proper; that is,
openaire   +1 more source

Explicit Spin Representations and Lie Algebras of Heisenberg Type

Journal of the London Mathematical Society, 1984
Let U and X be Euclidean spaces and \(\mu: U\times X\to X\) a normalized composition law, i.e. a bilinear mapping satisfying \(\| \mu(u,x)\| =\| u\| \cdot \| x\|,\) and such that for some \(u_ 0\), \(\mu(u_ 0,x)=x\) for all x. Let \(V=(u_ 0)^{\perp}\).
openaire   +2 more sources

2-Local derivations of Heisenberg–Virasoro type Lie algebras

Journal of Algebra and Its Applications
Let [Formula: see text] with [Formula: see text] be the Heisenberg–Virasoro type Lie algebras, and [Formula: see text] be a thin Lie algebra with only one diamond. In this paper, we study [Formula: see text]-local derivations on [Formula: see text] and [Formula: see text].
Chunguang Xia, Xiao Dong, Tianyu Ma
openaire   +2 more sources

Symplectic vector spaces and the Heisenberg Lie algebra

1980
Let V be a finite dimensional real vector space. Let B be a non-degenerate skew symmetric form on V. Hence dim V is even. Let dim V = 2n. Then we can choose a basis (P1, P2,..., Pn, Q1, Q2,..., Qn,) of V with the relations: $$\begin{array}{*{20}{c}} {B\left( {{{P}_{i}},{{P}_{j}}} \right) = 0}\\ {B\left( {{{P}_{i}},{{Q}_{j}}} \right) = {{\delta }_ ...
Gérard Lion, Michèle Vergne
openaire   +1 more source

On Extensions of Lie Algebras by Means of the Heisenberg Algebra

Mathematical Notes, 2005
We prove that extensions of an arbitrary algebra generated by the Heisenberg algebra are inessential after factorization with respect to the center of the Heisenberg algebra. The extensions considered in the paper have a standard description in terms of a pair consisting of a representation and a cohomology class.
openaire   +1 more source

Variational algorithms for linear algebra

Science Bulletin, 2021
Xiaosi Xu, Jinzhao Sun, Suguru Endo
exaly