**Contemporary Mathematics**

Volume: 652;
2015;
242 pp;
Softcover

MSC: Primary 17; 16;

**Print ISBN: 978-1-4704-1023-0
Product Code: CONM/652**

List Price: $112.00

AMS Member Price: $89.60

MAA Member Price: $100.80

**Electronic ISBN: 978-1-4704-2815-0
Product Code: CONM/652.E**

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# Lie Algebras and Related Topics

Share this page *Edited by *
*Marina Avitabile; Jörg Feldvoss; Thomas Weigel*

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.

#### Readership

Graduate students and research mathematicians interested in Lie theory, quantum groups, and representation theory.

# Table of Contents

## Lie Algebras and Related Topics

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- List of Talks xi12 free
- Grading Switching for Modular Non-Associative Algebras 114 free
- Gradings by Groups on Cartan Type Lie Algebras 1528
- 1. Introduction 1528
- 2. General facts about gradings 1629
- 3. Cartan type Lie algebras and their standard gradings 2033
- 4. Melikyan algebras and their standard gradings 2437
- 5. Gradings by groups without 𝑝-torsion. Cases 𝑊,𝑆,𝐻,𝐾. 2639
- 6. Gradings by groups without 𝑝-torsion. Case of Melikyan algebras 3447
- 7. Gradings by arbitrary abelian groups on restricted Cartan type Lie algebras 3750
- References 4558

- Simple Locally Finite Lie Algebras of Diagonal Type 4760
- Okubo Algebras: Automorphisms, Derivations and Idempotents 6174
- Constructing Semisimple Subalgebras of Real Semisimple Lie Algebras 7588
- Tilting Modules over the Path Algebra of Type \Aa, Polytopes, and Catalan Numbers 91104
- Lie Identities on Skew Elements in Group Algebras 103116
- Regular Derivations of Truncated Polynomial Rings 123136
- Lie Properties of Restricted Enveloping Algebras 141154
- 1. Introduction 141154
- 2. Notation and definitions 142155
- 3. The Lie structure of restricted enveloping algebras 143156
- 4. The group of units 144157
- 5. Lie nilpotency class 145158
- 6. Lie derived length 147160
- 7. Skew-symmetric and symmetric elements 149162
- 8. Ordinary enveloping algebras 150163
- References 151164

- Generic Semisimplicity of Reduced Enveloping Algebras 153166
- Modular Quantizations of Lie Algebras of Cartan Type 𝐻 via Drinfel’d Twists 173186
- Some Problems in the Representation Theory of Simple Modular Lie Algebras 207220
- Conjugacy of Nilpotent Elements in Characteristic 𝑝 229242
- Problems on Lie Properties of Skew and Symmetric Elements of Group Rings 231244
- Some Problems on Lie Properties of Restricted Enveloping Algebras 235248
- Open Questions on Modular Lie Algebras 237250
- Koszul Lie Algebras 241254
- Back Cover Back Cover1258