A degree theorem and decision methods for algebras of affine forms

Realization of locally extended affine Lie algebras of type $A_1$

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Structurable Tori

The classification of structurable tori with nontrivial involution, which was begun by Allison and Yoshii, is completed. New examples of struct-urable tori are obtained using a construction of structurable algebras from a semilinear version of cubic forms satisfying the adjoint identity. The classification uses techniques borrowed from quadratic forms over Z 2 and from the geometry of generaliz...

Affine Hecke Algebras of Type a and Their Cyclotomic Quotients

These are notes for a talk in the MIT-NEU Graduate seminar on Hecke Algebras and Affine Hecke Algebras (AHAHA) held in Fall 2014. This talk is divided into three parts. In the first, we introduce the affine Hecke algebras and describe a useful basis for the algebra over the ground ring. We then give a complete description of the center of the affine Hecke algebra and prove Kato’s Theorem regard...

The Multiplication Theorem and Bases in Finite and Affine Quantum Cluster Algebras

We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in [19]. Moreover some ZP-bases in quantum cluster algebras of finite and affine types are constructed. Under the specialization q and coefficients to 1, these bases are the integral bases of cluster algebra of finite and affine type...