Polarized Associative Algebras1

Poisson and Hamiltonian Superpairs over Polarized Associative Algebras1

Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic Poisson superpairs over a semi-finitely-filtered polarized Z2-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in t...

Block Idempotents of Twisted Group Algebras1

In [4] Conlon has successfully generalized much of the theory of modular representations to the projective case. However his generalization [4, p. 166] of one of Brauer's main theorems on blocks [3, 10B], [5] is not entirely satisfactory. In Theorem 1 we present another generalization which is closer than Conlon's to the original Brauer theorem, and in Theorem 2 we indicate an application invol...

A Note on the Representations of Nilpotent Lie Algebras1

A Method for Constructing Dirichlet Algebras1

The Non-associativity of Polarized Tree-Based Grammars

Polarities are used to sanction grammar fragment combination in high level tree-based formalisms such as eXtenssible MetaGrammar (XMG) and polarized unification grammars (PUG). We show that attaching polarities to tree nodes renders the combination operation non-associative, and in practice leads to overgeneration. We first provide some examples of non-associative combination operators in exist...