相关论文: Duality and Representations for New Exotic Bialgeb…

It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for…

An enhanced algebraic group $\uG$ of $G=\GL(V)$ over $\bbc$ is a product variety $\GL(V)\times V$, endowed with an enhanced cross product. Associated with a natural tensor representation of $\uG$, there are naturally Levi and parabolic…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

We construct a set of noncommuting translation operators in two and high-dimensional lattices. The algebras they close are $w_{\infty}$-algebras. The construction is based on the introduction of noncommmuting elementary link operators which…

Let R: V x V -> V x V be a Hecke type solution of the quantum Yang-Baxter equation (a Hecke symmetry). Then, the Hilbert-Poincre' series of the associated R-exterior algebra of the space V is a ratio of two polynomials of degree m…

Representations of two bridge knot groups in the isometry group of some complete Riemannian 3-manifolds as $E^{3}$ (Euclidean 3-space), $H^{3}$ (hyperbolic 3-space) and $ E^{2,1}$ (Minkowski 3-space), using quaternion algebra theory, are…

We review a new perspective on higher-spin holography, whereby Vasiliev's 4D higher-spin gravity emerges together with a 3D counterpart, consisting of coloured conformal matter fields coupled to topological conformal higher-spin and colour…

We generalize recent construction of four-dimensional $\mathcal{N}=1$ SCFT from wrapping six-dimensional $\mathcal{N}=(2,0)$ theory on a Riemann surface to the case of $D$-type with outer-automorphism twists. This construction allows us to…

In this paper we consider some global constructions of liftings of automorphic representations attached to some commuting pairs in the exceptional group $F_4$. We consider two families of integrals. The first uses the minimal representation…

We discuss recent developments in the study of semiorthogonal decompositions of algebraic varieties with an emphasis on their behaviour in families. First, we overview new results concerning homological projective duality. Then we introduce…

This monograph starts with an upper triangular matrix with integer entries and 1's on the diagonal. It develops from this a spectrum of structures, which appear in different contexts, in algebraic geometry, representation theory and the…

We describe the complete set of pairwise non-isomorphic irreducible modules S(a) over the algebra R given by the defining relation xy-yx=yy, and the rule how they could be glued to indecomposables. Namely, we show that Ext_k^1(S(a),S(b))=0,…

In this research we obtain the classical r-matrices of real two and three dimensional Jacobi-Lie bialgebras. In this way, we classify all non-isomorphic real two and three dimensional coboundary Jacobi-Lie bialgebras and their types…

Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is transcendental. This is a ring theoretic formulation of the well…

By using the relation between foliations and exotic R^4, orbifold $K$-theory deformed by a gerbe can be interpreted as coming from the change in the smoothness of R^4. We give various interpretations of integral 3-rd cohomology classes on…

All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…

In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of \lambda-circulant and \lambda-reverse circulant matrices. By using the constructions on…

We investigate the deformations and rigidity of boundary Heisenberg-like algebras. In particular, we focus on the Heisenberg and $\text{Heisenberg}\oplus\mathfrak{witt}$ algebras which arise as symmetry algebras in three-dimensional gravity…

In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…

We report some observations concerning two well-known approaches to construction of quantum groups. Thus, starting from a bialgebra of inhomogeneous type and imposing quadratic, cubic or quartic commutation relations on a subset of its…