Classical Lie Algebras at Infinity by Ivan Penkov
Preface.- Notation and Terminology. - I. Structure of Locally Reductive Lie Algebras.- 1. Finite-dimensional Lie algebras.- 2. Finite-dimensional Lie superalgebras.- 3. Root-reductive Lie algebras.- 4. Two generalizations.- 5. Splitting Borel subalgebras of sl(infinity), frak o (infinity), sp(infinity) and generalized flags.- 6. General Cartan, Borel and parabolic subalgebras of gl(infinity) and sl(infinity).- II. Modules over Locally Reductive Lie Algebras.- 7. Tensor modules of sl(infinity), frak o(infinity), sp (infinity).- 8. Weight modules.- 9.Generalized Harish-Chandra modules.- III. Geometric aspects. - 10.The Bott-Borel-Weil Theorem.- References.- Index of Notation.- Index.“The book is self-contained in an introductory way, it would be better for the reader to know the basics of Lie algebras and their representations… the book is most suitable for advanced graduate students and research mathematicians.” (Chengkang Xu, Mathematical Reviews, October, 2022)
“Classical Lie Algebras at Infinity is a very interesting book by I. Penkov and C. Hoyt. … Plenty of exercises of various levels of difficulty and open problems are given throughout the book. This exposition is an invitation to a wide open area of research, aiming to invoke a complex combination of advanced mathematical ideas.” (Mee Seong Im, zbMATH 1490.17025, 2022)
“The book is designed to not only serve as a reference but also to introduce well-prepared people to the subject and its current areas of inquiry. … it seems fair to say that this book will appeal to a somewhat narrower subset of readers of this column than do many of the books reviewed here. But the people in this subset should find this a useful, in the authors’ words, ‘invitation to a wide open research area’.” (Mark Hunacek, MAA Reviews, August 1, 2022)| SKU | Unavailable |
| ISBN 13 | 9783030896591 |
| ISBN 10 | 3030896595 |
| Title | Classical Lie Algebras at Infinity |
| Author | Ivan Penkov |
| Series | Springer Monographs In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer Nature Switzerland AG |
| Year published | 2022-01-06 |
| Number of pages | 239 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |