on generalized reduced representations of restricted lie superalgebras in prime characteristic

نویسندگان

y. f. yao

y. y. li

چکیده

let $mathbb{f}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted lie superalgebra over $mathbb{f}$. it is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. these quotient superalgebras are called the generalized reduced enveloping superalgebras, which generalize the notion of reduced enveloping superalgebras. properties and representations of these generalized reduced enveloping superalgebras are studied. moreover, each such superalgebra can be identified as a reduced enveloping superalgebra of the associated restricted lie superalgebra.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On generalized reduced representations of restricted Lie superalgebras in prime characteristic

Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...

متن کامل

Representations of Lie Superalgebras in Prime Characteristic I

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p > 2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a mixture of p-power and 2-power divisibilities of dimensions of modules. We establish the Conjecture for basic classical Lie superalgebras.

متن کامل

Typical Blocks of Lie Superalgebras in Prime Characteristic

For a type I basic classical Lie superalgebra g = g0̄⊕g1̄, we establish an equivalence between typical blocks of categories of Uχ(g)-modules and Uχ(g0̄)modules. We then deduce various consequences from the equivalence.

متن کامل

Representations of Lie Superalgebras in Prime Characteristic Ii: the Queer Series

The modular representation theory of the queer Lie superalgebra q(n) over characteristic p > 2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters χ and a criterion for the semisimplicity of the corresponding reduced enveloping algebras Uχ(q(n)). A (2p)-power divisibility of dimensions of q(n)-modules with nilpotent p-characters is estab...

متن کامل

REPRESENTATIONS OF RESTRICTED LIE ALGEBRAS OF CHARACTERISTIC p

It was proved by Jacobson [2] that every finite-dimensional Lie algebra of characteristic p has a finite-dimensional representation space which is not semisimple. In this note we prove a similar result for Jacobson's restricted Lie algebras [l]. The structure of a restricted Lie algebra L over a field F of characteristic p comprises, in addition to the ordinary Lie algebra structure, a map x—*-...

متن کامل

Universally defined representations of Lie conformal superalgebras

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined representation of a conformal Lie (super)algebra L is completely determined by commutation relations of L and by the requirement of associative locality of generators. W...

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید


عنوان ژورنال:
bulletin of the iranian mathematical society

ناشر: iranian mathematical society (ims)

ISSN 1017-060X

دوره 41

شماره 5 2015

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023