Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · q-alg/9504023

Quantum planes and quantum cylinders from Poisson homogeneous spaces

N. Ciccoli
View original source ↗Read source document ↗Export metadata ↓

Abstract

Quantum planes and a new quantum cylinder are obtained as quantization of Poisson homogeneous spaces of two different Poisson structures on classical Euclidean group E(2).

Explore related subjects

q-algmath.QA

Keep this discovery

BibTeXRIS

N. Ciccoli. 1995-04-25. Quantum planes and quantum cylinders from Poisson homogeneous spaces. https://doi.org/10.1088/0305-4470%2F29%2F7%2F018

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2005

Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity

We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive N-th root of unity. For general four-parameter AWP, zeros of the N-th polynomial and the orthogonality measure are found explicitly. Special subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi polynomials, are considered in detail. A set of discrete weight functions positive on a real interval is described. Some new trigonometric identities related to the AWP are obtained. Normalization conditions of some polynomials are expressed in terms of the Gauss sums.

q-alg↗
arXiv2005

SL(2,Z)-Invariant Spaces Spanned by Modular Units

Characters of rational vertex operator algebras (RVOAs) arising in 2-dimensional conformal field theories often belong (after suitable normalization) to the (multiplicative) semigroup E^+ of modular units whose Fourier expansions are in 1+q Z_{>=0}[[q]], up to a fractional power of q. If even all characters of a RVOA share this property then we have an example of what we call modular sets, i.e. finite subsets of E^+ whose elements (additively) span a vector space which is invariant under the usual action of SL(2,Z). The classification of modular sets and RVOAs seem to be closely related. In this article we give an explicit description of the group of modular units generated by E^+, we prove a certain finiteness result for modular sets contained in a natural semi-subgroup E_* of E^+, and we discuss consequences.

q-alg↗
arXiv2004

Higher-dimensional Algebra and Topological Quantum Field Theory

The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional TQFTs are to be described as n-category representations. First we describe a "suspension" operation on n-categories, and hypothesize that the k-fold suspension of a weak n-category stabilizes for k >= n+2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n-dimensional unitary extended TQFTs as weak n-functors from the "free stable weak n-category with duals on one object" to the n-category of "n-Hilbert spaces". We conclude by describing n-categorical generalizations of deformation quantization and the quantum double construction.

q-alg↗