A depth two extension A | B is shown to be weak depth two over its double centralizer V A (V A (B)) if this is separable over B. We introduce a notion of codepth two coalgebra homomorphism g : C → D, dual to a depth two algebra homomorphism. It is shown that the endomorphism ring of bicomodule endomorphisms End D C D forms a right bialgebroid over the centralizer subalgebra g * : D * → C * of t...

The following basic results on infinite locally finite subgroups of a free m-generŽ . 48 ator Burnside group B m, n of even exponent n, where m ) 1 and n G 2 , n is divisible by 29, are obtained: A clear complete description of all infinite groups that Ž . Ž . are embeddable in B m, n as maximal locally finite subgroups is given. Any Ž . infinite locally finite subgroup L of B m, n is contained...

Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the action of a complex reductive Lie algebra g on tensor space of the form M ⊗ N ⊗ V ⊗k. We define the degenerate two-boundary braid group Gk and show that centrali...

Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...

The enveloping algebra U(g) of the Lie superalgebra g has a deformation, called the Yangian of qN . For each M = 1 ,2 , . . . denote by A M N the centralizer of qM ⊂ qN+M in the associative superalgebra U(qN+M ) . We construct a sequence of surjective homomorphisms U(qN ) ← A 1 N ← A 2 N ← . . . . We describe the inverse limit of the sequence of centralizer algebras A1N ,A 2 N , . . . in terms ...

Let G be the adjoint group of a simple Lie algebra g, and let KC ! Aut(pC) be the complexi ed isotropy representation at the identity coset of the corresponding symmetric space. If e 2 pC is nilpotent, we consider the centralizer of e in KC. We show that the conjugacy classes of the component group of this centralizer can be described in terms generalizing the Bala-Carter classi cation of nilpo...