Automorphisms of infinite dimensional Lie algebras of Cartan type

In this paper it is proved that any automorphism of an infinite dimensional Lie algebra of Cartan type over an algebraically closed field of characteristicp>2 can be induced from an automorphism of the associated divided power algebra.     

一类新无限维李子代数的同构和同态

构造了一类由三个基本元生成的无限维李代数.证明了这类无限维李代数是Virasoro-like李代数的推广.此外,研究了这类李子代数同构和同态.     

An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension

The famous 1960's construction of Golod and Shafarevich yields infinite dimensional nil, but not nilpotent, algebras. However, these algebras have exponential growth. Here, we construct an infinite dimensional nil, but not locally nilpotent, algebra which has polynomially bounded growth.

     

Automorphisms of the algebra ofq-difference operators

In this paper, automorphisms of the algebra ofq-difference operators, as an associative algebra for arbitraryq and as a Lie algebra forq being not a root of unity, are determined. Project supported by the NNSF of China     

Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology

The mod 2 Steenrod algebra and Dyer-Lashof algebra have both striking similarities and differences arising from their common origins in ``lower-indexed' algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra , whose module actions are equivalent to, but quite different from, those of and . The exact relationships emerge as ``sheared algebra bijections', which also illuminate the role of the cohomology of . As a bialgebra, has a particularly attractive and potentially useful structure, providing a bridge between those of and , and suggesting possible applications to the Miller spectral sequence and the structure of Dickson algebras.

     

Actions of the dipper-donkin quantization GL 2 on the clifford algebra C(l,3)

Following the method already developed for studying the actions of GL_q (2,C) on the Clifford algebra C(l,3) and its quantum invariants [1], we study the action on C(l, 3) of the quantum GL ₂ constructed by Dipper and Donkin [2]. We are able of proving that there exits only two non-equivalent cases of actions with nontrivial “perturbation” [1]. The spaces of invariants are trivial in both cases.

We also prove that each irreducible finite dimensional algebra representation of the quantum GL ₂ q^m ≠1, is one dimensional.

By studying the cases with zero “perturbation” we find that the cases with nonzero “perturbation” are the only ones with maximal possible dimension for the operator algebra ?.     

Automorphisms of the Toeplitz algebra with piecewise continuous symbol

The automorphism group of the Toeplitz algebra generated by the Toeplitz operators, whose symbols are continuous functions on the circle beside finitely fixed points, is characterized.     

On the clifford index of a general (e+2)-gonal curve

^{b q} Both authors are grateful to the Korea Science and Engineering Foundation and the second author is grateful to the DaeWoo Foundation and the Ministry of Education-Korea, for partial support of this work.     

A mod 2 index theorem for pin~- manifolds

We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin~- manifolds. The analytic index is the reduced η invariant of(twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer(1971)to non-orientable manifolds.