We use Constraint Satisfaction Methods to construct and enumerate finite L L -algebras up isomorphism. These objects were recently intro...

This paper is the first of a series investigating the affine Birman-Wenzl-Murakami (BMW) algebras and their cyclotomic quotients. The purpose of this paper is to establish an isomorphism between the affine BMW algebras (defined by generators and relations) and the algebras of (n, n)–tangles in the solid torus, modulo Kauffman skein relations. The Birman-Wenzl-Murakami algebras were conceived in...

We develop an equivariant Dixmier-Douady theory for locally trivial bundles of C⁎-algebras with fibre D⊗K equipped a fibrewise T-action, where T denotes the circle group and D=End(V)⊗∞ T-representation V. In particular, we show that T-equivariant ⁎-automorphisms AutT(D⊗K) is infinite loop space giving rise to cohomology ED,T⁎(X). Isomorphism classes then form respect tensor product isomorphic E...

For certain AF algebras, a topological space is described which provides an isomorphism invariant for the algebras in this class. These AF algebras can be described in graphical terms by virtue of the existence of a certain type of Bratteli diagram, and the orderpreserving automorphisms of the corresponding AF algebra’s dimension group are then studied by utilizing this graph. This will also pr...

In this paper, first we show that the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphism between adjoint representation and coadjoint representation. Then introduce notions of relative Rota-Baxter operators on algebras pre-Lie-Yamaguti algebras. We prove gives rise to naturally operator algebra. Finally, study symplectic structures algebra, which give as well As ...

We consider algebras with a single n-ary operation and a certain type of associativity.We prove that up to isomorphism there are exactly 5 of these associative mono-n-ary algebras with 2 elements for even n ≥ 2 and 6 for odd n ≥ 3. These algebras are described explicitly. It is shown that a similar result is impossible for algebras with at least 4 elements. An application concerning the assignm...

We define united K-theory for real C*-algebras, generalizing Bousfield’s topological united K-theory. United K-theory incorporates three functors — real K-theory, complex K-theory, and self-conjugate K-theory — and the natural transformations among them. The advantage of united K-theory over ordinary K-theory lies in its homological algebraic properties, which allow us to construct a Künneth-ty...

We describe the finite-dimensional simple modules of all the twisted multiloop algebras and classify them up to isomorphism.