Search results for "Mathematics::Quantum Algebra"
showing 10 items of 77 documents
-Poincaré supergravities from Lie algebra expansions
2012
Abstract We use the expansion of superalgebras procedure (summarized in the text) to derive Chern–Simons (CS) actions for the ( p , q ) -Poincare supergravities in three-dimensional spacetimes. After deriving the action for the ( p , 0 ) -Poincare supergravity as a CS theory for the expansion osp ( p | 2 ; R ) ( 2 , 1 ) of osp ( p | 2 ; R ) , we find the general ( p , q ) -Poincare superalgebras and their associated D = 3 supergravity actions as CS gauge theories from an expansion of the simple osp ( p + q | 2 , R ) superalgebras, namely osp ( p + q | 2 , R ) ( 2 , 1 , 2 ) .
Perturbative BF-Yang–Mills theory on noncommutative
2000
A U(1) BF-Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is presented and in this formulation the U(1) Yang-Mills theory on noncommutative ${\mathbb{R}}^4$ is seen as a deformation of the pure BF theory. Quantization using BRST symmetry formalism is discussed and Feynman rules are given. Computations at one-loop order have been performed and their renormalization studied. It is shown that the U(1) BFYM on noncommutative ${\mathbb{R}}^4$ is asymptotically free and its UV-behaviour in the computation of the $\beta$-function is like the usual SU(N) commutative BFYM and Yang Mills theories.
Multiple Noncommutative Tori and Hopf Algebras
2001
We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.
On the Leibniz bracket, the Schouten bracket and the Laplacian
2003
International audience; The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them is obtained. Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie algebra structure. In particular, those algebras generated by the Leibniz bracket of the divergence and the Laplacian operators on the exterior algebra are considered, and the expression of the Laplacian for the product of two functions is generalized for arbitrary exterior forms.
Noncompact Topological Quantum Groups
1995
A star-product construction of quantum semisimple real Lie groups is performed for the noncompact case.
On Chiral Quantum Superspaces
2011
We give a quantum deformation of the chiral Minkowski superspace in 4 dimensions embedded as the big cell into the chiral conformal superspace. Both deformations are realized as quantum homogeneous superspaces: we deform the ring of regular functions together with a coaction of the corresponding quantum supergroup.
On the bicrossproduct structures for the family of algebras
1998
It is shown that the family of deformed algebras has a different bicrossproduct structure for each in analogy to the undeformed case.
Relative cohomology spaces for some osp($n|2$)-modules
2018
International audience; In this work, we describe the H-invariant, so(n)-relative cohomology of a natural class of osp(n|2)-modules M, for n ≠ 2. The Lie superalgebra osp(n|2) can be realized as a superalgebra of vector fields on the superline R1|n. This yields canonical actions on spaces of densities and differential operators on the superline. The above result gives the zero, first, and second cohomology spaces for these modules of densities and differential operators.
Singular quadratic Lie superalgebras
2012
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.
THE AMITSUR–LEVITZKI THEOREM FOR THE ORTHOSYMPLECTIC LIE SUPERALGEBRA osp(1, 2n)
2006
http://www.worldscinet.com/jaa/05/0503/S0219498806001740.html; International audience; Based on Kostant's cohomological interpretation of the Amitsur–Levitzki theorem, we prove a super version of this theorem for the Lie superalgebras osp(1, 2n). We conjecture that no other classical Lie superalgebra can satisfy an Amitsur–Levitzki type super identity. We show several (super) identities for the standard super polynomials. Finally, a combinatorial conjecture on the standard skew supersymmetric polynomials is stated.