The Drinfeld-Sokolov reduction method has been used to associate with gln extensions of the matrix r-KdV system. Reductions of these systems to the fixed point sets of involutive Poisson maps, implementing reduction of gln to classical Lie algebras of type B, C, D, are here presented. Modifications corresponding, in the first place to factorisation of the Lax operator, and then to Wakimoto real...

Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld–Jimbo quantum group U h g and is commutative with respect to an involutive operator˜S : A⊗A → A⊗A. Such a multiplication is unique. Let M be a kählerian symmetr...

Representation of the algebra of FP (anti)ghosts in string theory is studied by generalizing the recursive fermion system in the Cuntz algebra constructed previously. For that purpose, the pseudo Cuntz algebra, which is a ∗-algebra generalizing the Cuntz algebra and acting on indefinite-metric vector spaces, is introduced. The algebra of FP (anti)ghosts in string theory is embedded into the pse...

In this paper, we propose the concept of involutive direction ss a vector representation for the concept of involutive division proposed by Gerdt and hi co-workers. With this representation, most of the properties of involutive divisions such as Noetherity, Artinity, and constructivity, can be greatly simplified. A new algorithm to compute the involutive completion is also given. Based on the v...

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras. Their properties and connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. In this paper we study the class of perfect pseudo-BCK algebras with pseudo-product and we prove that any perfect pseudo-BCK algebra with pseudo-product is strongly bipartite. Anothe...

In this paper we describe an efficient involutive algorithm for constructing Gröbner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain way. In the presented algorithm a reduced Gröbner basis is the internally fixed subset of an involutive basis, and having computed the later, the former can be...

Involutive bases are a comparatively recent concept in commutative algebra. They have been introduced by Gerdt and Blinkov [3] based on ideas from the Janet-Riquier theory of differential equations. A gentle introduction into the basic ideas can be found in [1]; [5] presents the theory in full detail and extends it to a large class of non-commutative algebras including for example rings of line...