In this paper we explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and applying some properties of root vector decomposition we obtain their isomorphism theorem. AMS Classification: 17B05; 17B30

Recently Daviau showed the equivalence of ordinary matrix based Dirac theory –formulated within a spinor bundle Sx ≃ C 4 x–, to a Clifford algebraic formulation within space Clifford algebra Cl(R, δ) ≃ M2(C) ≃ P ≃ Pauli algebra (matrices) ≃ H ⊕ H ≃ biquaternions. We will show, that Daviau’s map θ : C 7→ M2(C) is an isomorphism. Furthermore it is shown that Hestenes’ and Parra’s formulations are...

A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole of order 2. The algebra is shown to be isomorphic to the Birman-Murakami-Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which, in our set-up, occurs when the Coxeter type is An−1. The proof involves a diagrammatic version o...

One of the basic properties of the Clifford algebra gives an explicit basis for it in terms of a basis of the underlying vector space (Theorem 1 below), and another one provides a vector space isomorphism between the Clifford algebra and the exterior algebra of the same vector space (the so-called Chevalley map, Theorem 2 below). While both of these properties appear in standard literature such...

In [8], V.G. Drinfeld gave a new set of generators and relations for the quantum affine algebra Uq(ĝ) (and also for the Yangian). He also gave an isomorphism between the two realizations, but there was no proof in that article. In [1], J. Beck found these new generators inside Uq(ĝ), and proved that they satisfy the relations given by Drinfeld. He also proved that the two realizations were isom...

In this paper, we study a family of C*-subalgebras defined by fixed points generalized gauge actions Cuntz–Krieger algebra introducing étale groupoids whose associated C*-algebras are these C*-subalgebras. We show that topological conjugacy classes one-sided Markov shifts characterized in terms the isomorphism groupoids.

Let Γ(x0) be a finite rooted tree, for which Γ is the underlying tree and x0 root. T Terwilliger algebra of with respect to x0. We study structure principal T-module. As result, it shown that recognizes isomorphism class Γ(x0).

Let G be a connected reductive group over an algebraically closed field K of characteristic 0, X an affine symplectic variety equipped with a Hamiltonian action of G. Further, let ∗ be a G-invariant Fedosov star-product on X such that the Hamiltonian action is quantized. We establish an isomorphism between the center of the quantum algebra K[X ][[~]] and the algebra of formal power series with ...

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such algebra g, we describe space structures on g up to isomorphism. As an application, having non-trivial abelian J-invariant ideal are classified dimensions.

It is well known that a measured groupoid G defines a von Neu-mann algebra W * (G), and that a Lie groupoid G canonically defines both a C *-algebra C * (G) and a Poisson manifold A * (G). We show that the maps (G) are functorial with respect to suitable categories. In these categories Morita equivalence is isomorphism of objects, so that these maps preserve Morita equivalence.