Let R be the Z-module generated by the irreducible characters of the symmetric group Sd . We determine bases for the kernel of the decomposition map. It is known that R ⊗Z F is isomorphic to the radical quotient of the Solomon descent algebra when F is a field of characteristic zero. We show that when F has prime characteristic and I d br is the kernel of the decomposition map for prime p then ...

In this paper we give an axiom system of a non-linear 4-valued logic which we call a de Morgan logic (ML), whose Lindenbaum algebra is the de Morgan algebra with implication (MI-algebra), and show that (1) For every MI-algebra L, there is a quotient MI-algebra L such that it is embeddable to the simplest 4-valued MI-algebra M = {0, a, b, 1}; (2) The Lindenbaum algebra of ML is the MI-algebra; (...

We show that there is a computable Boolean algebra B and a computably enu-merable ideal I of B such that the quotient algebra B=I is of Cantor{Bendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of innnite Cantor{Bendixson rank.

We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra B=I is of Cantor{Bendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of in nite Cantor{Bendixson rank.

We describe an effective algorithm to determine the maximal class-c quotient (or the maximal commutative class-c quotient) of a finitely presented associative algebra over an arbitrary field. As application, we investigate the relatively free d-generator algebras satisfying the identity xn = 0. In particular, we consider the identity x = 0 and the cases (d, n) = (2, 4) and (d, n) = (2, 5).

Let G be a simple complex Lie group, g be its Lie algebra, K be a maximal compact form of G and k be a Lie algebra of K. We denote by X → X the anti-involution of g which singles out the compact form k. Consider the space of flat g-valued connections on a Riemann sphere with three holes which satisfy the additional condition A(z) = −A(z). We call the quotient of this space over the action of th...

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W , we show that the Chevalley morphism π : t/W → g/G is an isomorphism except for the group Sp2n over a base with 2-torsion...

We study the representation theory of braids and ties algebra, or bt -algebra, E n ( q ) . Using cellular basis { m s t } for obtained in previous joint work with J. Espinoza we introduce two kinds permutation modules M λ Λ show that tensor product module V ⊗ is a direct sum 's. dual its action on annihilator ideal I enjoys nice compatibility property respect to finally quotient algebra / , sho...

Let C(X) be the algebra generated by the curvature two-forms of standard holomorphic hermitian line bundles over the complex homogeneous manifold X = G/B. The cohomology ring of X is a quotient of C(X). We calculate the Hilbert polynomial of this algebra. In particular, we show that the dimension of C(X) is equal to the number of independent subsets of roots in the corresponding root system. We...

Let C(X) be the algebra generated by the curvature two-forms of standard holomorphic hermitian line bundles over the complex homogeneous manifold X = G/B. The cohomology ring of X is a quotient of C(X). We calculate the Hilbert polynomial of this algebra. In particular, we show that the dimension of C(X) is equal to the number of independent subsets of roots in the corresponding root system. We...