Search results for "Mathematics::Quantum Algebra"
showing 10 items of 77 documents
Algebra Structures on Hom(C,L)
1999
info:eu-repo/semantics/published
BASIC TWIST QUANTIZATION OF osp(1|2) AND κ-DEFORMATION OF D = 1 SUPERCONFORMAL MECHANICS
2003
The twisting function describing a nonstandard (super-Jordanian) quantum deformation of $osp(1|2)$ is given in explicite closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed $osp(1|2)$ superalgebras are considered. One real quantum $osp(1|2)$ superalgebra is interpreted as describing the $\kappa$-deformation of D=1, N=1 superconformal algebra, which can be applied as a symmetry algebra of N=1 superconformal mechanics.
DEFORMATION QUANTIZATION OF COADJOINT ORBITS
2000
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
Hopf algebras, renormalization and noncommutative geometry
1998
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
The Minkowski and conformal superspaces
2006
We define complex Minkowski superspace in 4 dimensions as the big cell inside a complex flag supermanifold. The complex conformal supergroup acts naturally on this super flag, allowing us to interpret it as the conformal compactification of complex Minkowski superspace. We then consider real Minkowski superspace as a suitable real form of the complex version. Our methods are group theoretic, based on the real conformal supergroup and its Lie superalgebra.
On the maximal superalgebras of supersymmetric backgrounds
2009
17 pages.-- ISI article identifier:000262585300016.-- ArXiv pre-print avaible at:http://arxiv.org/abs/0809.5034
Quantum and Braided Integrals
2001
We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces while presenting some new results as well. A rather detailed discussion outlines the motivation for adopting the Hopf algebra language. We then present some trace formulas for the integral on Hopf algebras and show how to treat the $\int 1=0$ case. We extend the discussion to braided Hopf algebras relying on diagrammatic techniques. The use of the general formulas is illustrated by explicitly worked out examples.
Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)
2003
We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).
The HOMFLY-PT polynomials of sublinks and the Yokonuma–Hecke algebras
2016
We describe completely the link invariants constructed using Markov traces on the Yokonuma-Hecke algebras in terms of the linking matrix and the HOMFLYPT polynomials of sublinks.
Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
2015
We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.