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We give a necessary and sufficient PBW basis criterion for Hopf algebras generated by skew-primitive elements and abelian group of group-like elements with action given via characters. This class of ...
Remarks on Cyclotomic and Degenerate Cyclotomic BMW Algebras
Degenerate Cyclotomic BMW Algebras math
2010/11/19
We relate the structure of cyclotomic and degenerate cyclotomic BMW algebras, for arbitrary parameter values, to that for admissible parameter values. In particular, we show that these algebras are ce...
On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension Four
Hilbert Functions Gorenstein Artin Algebras
2010/11/18
We prove that the Hilbert functions of codimension four graded Gorenstein Artin algebras R/I are unimodal provided I has a minimal generator in degree less than five. It is an open question whether al...
Arens regularity of module actions and weak amenability of Banach algebras
Arens regularity weak amenability of Banach algebras
2010/11/9
For Banach left and right module actions, we will establish the relationships between topological centers of module actions with some result in the weak amenability of Banach algebras.
The representation dimension of Hecke algebras and symmetric groups
Hecke algebras symmetric groups
2010/11/22
We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A, B and D. For all the type A algebras, and most of the algebras of types B and D, we also es...
Super-Poincare' algebras, space-times and supergravities (I)
Super-Poincare' algebras space-times supergravities
2010/11/18
A new formulation of theories of supergravity as theories satisfying a generalized Principle of General Covariance is given. It is a generalization of the superspace formulation of simple 4D-supergra...
Diassociative algebras and Milnor's invariants for tangles
Diassociative algebras Milnor's invariants
2010/11/8
We extend Milnor's mu-invariants of link homotopy to ordered tangles. Simple combinatorial formulas for mu-invariants are given in terms of counting trees in Gauss diagrams. Invariance under Reidemei...
Hilbert series of PI relatively free G-graded algebras are rational functions
free G-graded algebras rational functions
2010/11/19
Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F be the corresponding free...
Meander graphs and Frobenius Seaweed Lie algebras
Meander graphs Frobenius Seaweed Lie algebras
2010/11/11
The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this graph in several ways with a goal of determining families of Frobenius (index zero) seaweed algebr...
Arens Regularity of Tensor Products and Weak Amenability of Banach Algebras
Arens Regularity of Tensor Products Weak Amenability of Banach Algebras
2010/11/9
In this note, we study the Arens regularity of projective tensor product $A\hat{\otimes}B$ whenever $A$ and $B$ are Arens regular. We establish some new conditions for showing that the Banach algebra...
The (G, \theta)-Lie algebras are structures which unify the Lie algebras and Lie superalgebras. We use them to produce solutions for the quantum Yang-Baxter equation. The constant and the spectral-par...
Let $\pi, \pi'$ be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincar\'e pairing $EP (\pi,\pi')$, the alternating sum of the dimensions of the...
Krall-Jacobi commutative algebras of partial differential operators
Krall-Jacobi commutative algebras partial differential operators
2010/11/18
We construct a large family of commutative algebras of partial differential operators invariant under rotations. These algebras are isomorphic extensions of the algebras of ordinary differential oper...
Direct Construction of Grassmann, Clifford and Geometric Algebras
Direct Construction of Grassmann Clifford and Geometric Algebras
2010/11/22
This is a simple way rigorously to construct Grassmann, Clifford and Geometric Algebras, allowing degenerate bilinear forms, infinite dimension, using fields or certain modules (characteristic 2 with ...
On the conjugacy of pure imaginary elements of quaternion algebras and Cayley algebras
quaternion algebras Cayley algebras
2010/11/9
In the quatenions ($\H$, $\H'$, $\H^{C}$) and octonions ($\gC$, $\gC^\prime$, $\gC^C$), we show some results on the conjugacy of two pure imaginary non-zero elements with same norm.