Related papers: Quantum groups and interacting quantum fields
We investigate symmetries of the scalar field theory with harmonic term on the Moyal space with euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on…
Given a C*-algebra B, a closed *-subalgebra A contained in B, and a partial isometry S in B which "interacts" with A in the sense that S*aS = H(a)S*S and SaS* = V(a)SS*, where V and H are positive linear operators on A, we derive a few…
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Multi-parameter versions U_p(g) and C_p[G] of the standard quantum groups U_q(g) and C_q[G] are considered where G is a semi-simple connected complex algebraic group and g is the Lie algebra of G. The primitive spectrum of C_p[G] is…
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…
We describe geometrically the classical and quantum inhomogeneous groups $G_0=(SL(2, \BbbC)\triangleright \BbbC^2)$ and $G_1=(SL(2, \BbbC)\triangleright \BbbC^2)\triangleright \BbbC$ by studying explicitly their shape algebras as a spaces…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
{\sc CLIFFORD} is a Maple package for computations in Clifford algebras $\cl (B)$ of an arbitrary symbolic or numeric bilinear form B. In particular, B may have a non-trivial antisymmetric part. It is well known that the symmetric part g of…
The aim of this paper is to provide an answer to the $\mathbb{C}[\partial]$-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on $E=R\oplus Q$ up to…
In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…
We construct integrable Hamiltonian systems with Lie bialgebras $({\bf g} , {\bf \tilde{g}})$ of the bi-symplectic type for which the Poisson-Lie groups ${\bf G}$ play the role of the phase spaces, and their dual Lie groups ${\bf {\tilde…
Suppose $D$ is a finite dimensional C*-algebra carrying a continuous action $\overline{\Pi}$ of the circle group $\mathbb{T}$. We study the quantum symmetry group of $D$, taking $\overline{\Pi}$ into account. We show that they are braided…
By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the…
The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable sequences is a Cayley-Dickson algebra.
Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…
Let $\mathfrak g$ be a symmetrizable Kac-Moody Lie algebra, and let $V_{\hat{\mathfrak g},\hbar}^\ell$, $L_{\hat{\mathfrak g},\hbar}^\ell$ be the quantum affine vertex algebras constructed in [11]. For any complex numbers $\ell$ and…
A sort of calculus is developed to find the chiral algebras of N=2 superconformal interacting bosonic models. Many examples are discussed. It is shown that the algebras share a common structure, which we call almost Landau Ginzburg. For one…
A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras…
The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C(0,2). This algebra is essentially the geometric algebra…
Let A be a C*-algebra, h a Hilbert space and C the CAR algebra over h. We construct a twisted tensor product of A by C such that the two factors are not necessarily one in the relative commutant of the other. The resulting C*-algebra may be…