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New Lie tori from Naoi tori
Yoji Yoshii
We define general Lie tori which generalize original Lie tori. We show that a Naoi torus is a general Lie torus. We give examples and prove several properties of general Lie tori.…
Locally loop algebras and locally affine Lie algebras
Jun Morita, Yoji Yoshii
We investigate a new class of Lie algebras, which are tame locally extended affine Lie algebras of nullity 1. It is an infinite-rank analog of affine Lie algebras, and their center…
Structurable Tori
Bruce Allison, John Faulkner, Yoji Yoshii
The classification of structurable tori with nontrivial involution, which was begun by Allison and Yoshii, is completed. New examples of structurable tori are obtained using a cons…
Cayley Polynomials
Yoji Yoshii
We consider a polynomial version of the Cayley numbers. Namely, we define the ring of Cayley polynomials in terms of generators and relations in the category of alternative algebra…
Lie G-Tori of Symplectic Type
Georgia Benkart, Yoji Yoshii
We classify centerless Lie G-tori of type C_r including the most difficult case r=2 by applying techniques due to Seligman. In particular, we show that the coordinate algebra of a…
Locally extended affine Lie algebras
Jun Morita, Yoji Yoshii
We propose a new simplified definition of extended affine Lie algebras (EALAs for short), and also discuss a general version of extended affine Lie algebras, called locally extende…