Lie algebras and related topics : workshop on lie algebras in honor of Helmut Strade's 70th birthday, May 22-24, 2013, Università degli studi di Milano-Bicocca, Milano, Italy / Marina Avitabile, Jörg Feldvoss, Thomas Weigel, editors.

Format:

Book

Contributor:

Strade, Helmut, 1942- honouree.

Avitabile, Marina, 1971- editor.

Feldvoss, Jörg, 1960- editor.

Weigel, Thomas (Thomas S.), editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 652

Contemporary mathematics, 652 0271-4132

Language:

English

Subjects (All):

Lie algebras--Congresses.

Lie algebras.

Physical Description:

1 online resource (258 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2015]

Language Note:

English

Summary:

This volume contains the proceedings of the Workshop on Lie Algebras, in honor of Helmut Strade's 70th Birthday, held from May 22-24, 2013, at the Università degli Studi di Milano-Bicocca, Milano, Italy. Lie algebras are at the core of several areas of mathematics, such as, Lie groups, algebraic groups, quantum groups, representation theory, homogeneous spaces, integrable systems, and algebraic topology. The first part of this volume combines research papers with survey papers by the invited speakers. The second part consists of several collections of problems on modular Lie algebras, their representations, and the conjugacy of their nilpotent elements as well as the Koszulity of (restricted) Lie algebras and Lie properties of group algebras or restricted universal enveloping algebras.

Contents:

Cover

Title page

Contents

Preface

List of Talks

Grading Switching for Modular Non-Associative Algebras

1. Introduction

2. Artin-Hasse exponentials of derivations

3. Laguerre polynomials of derivations

4. Applications

References

Gradings by Groups on Cartan Type Lie Algebras

2. General facts about gradings

3. Cartan type Lie algebras and their standard gradings

4. Melikyan algebras and their standard gradings

5. Gradings by groups without -torsion. Cases , , , .

6. Gradings by groups without -torsion. Case of Melikyan algebras

7. Gradings by arbitrary abelian groups on restricted Cartan type Lie algebras

Simple Locally Finite Lie Algebras of Diagonal Type

2. Local and inductive systems

3. Proof of the main theorem

Okubo Algebras: Automorphisms, Derivations and Idempotents

2. Okubo algebras

3. Derivations

4. Automorphisms

5. Idempotents

Constructing Semisimple Subalgebras of Real Semisimple Lie Algebras

2. Preliminaries

3. Construction of embeddings

4. Implementation and examples

5. -subalgebras of the exceptional Lie algebras

Tilting Modules over the Path Algebra of Type \Aa, Polytopes, and Catalan Numbers

2. Representations of \Aa_{ }

3. Proofs of Theorems 1.1-1.3

4. Proofs of Theorems 1.4 and 1.5

5. Tilting sequences

6. Some further comments

Lie Identities on Skew Elements in Group Algebras

2. Definitions and classical results

3. Lie nilpotent skew elements

4. Bounded Lie Engel skew elements

5. Lie solvable skew elements

6. Skew elements of torsion groups without dihedral involvement

Acknowledgement

References.

Regular Derivations of Truncated Polynomial Rings

2. Generalities and recollections

3. Characterising regular derivations of \OO_{ }

4. Dickson invariants and the fibres of

Acknowledgements

Lie Properties of Restricted Enveloping Algebras

2. Notation and definitions

3. The Lie structure of restricted enveloping algebras

4. The group of units

5. Lie nilpotency class

6. Lie derived length

7. Skew-symmetric and symmetric elements

8. Ordinary enveloping algebras

Generic Semisimplicity of Reduced Enveloping Algebras

1. Some facts related to generic semisimplicity

2. Solvable Lie algebras

3. Recognition of generic semisimplicity by a simple block

4. Variation of the numeric invariants in a family of algebras

Modular Quantizations of Lie Algebras of Cartan Type via Drinfel'd Twists

1. Preliminaries

2. Drinfel'd twists over ( )[[ ]]

3. Quantizations of vertical type for Lie bialgebras of Cartan type

4. Quantizations of horizontal type for Lie bialgebras of Cartan type

Some Problems in the Representation Theory of Simple Modular Lie Algebras

2. Background and notation

3. A dozen related problems

4. Evidence for Conjecture 3.4 and a related conjecture

Conjugacy of Nilpotent Elements in Characteristic

Problems on Lie Properties of Skew and Symmetric Elements of Group Rings

Some Problems on Lie Properties of Restricted Enveloping Algebras

Open Questions on Modular Lie Algebras

Koszul Lie Algebras

Back Cover.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-2815-6