東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ subject:"Topological Groups and Lie Groups." ]

切換: 標籤 | MARC模式 | ISBD

Classical lie algebras at infinity

Penkov, Ivan.

FindBook

Google Book

Amazon

博客來

Classical lie algebras at infinity

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Classical lie algebras at infinity/ by Ivan Penkov, Crystal Hoyt.
作者:	Penkov, Ivan.
其他作者:	Hoyt, Crystal.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xiii, 239 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Lie algebras. -
電子資源:	https://doi.org/10.1007/978-3-030-89660-7
ISBN:	9783030896607

Classical lie algebras at infinity
Penkov, Ivan.

Classical lie algebras at infinity[electronic resource] /by Ivan Penkov, Crystal Hoyt. - Cham :Springer International Publishing :2022. - xiii, 239 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

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.

Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.

ISBN: 9783030896607

Standard No.: 10.1007/978-3-030-89660-7doiSubjects--Topical Terms:

526115
Lie algebras.

LC Class. No.: QA252.3 / .P46 2022

Dewey Class. No.: 512.482

Classical lie algebras at infinity
LDR:03008nmm a2200337 a 4500 001 2297561
003 DE-He213
005 20220112012327.0
006 m d
007 cr nn 008maaau
008 230324s2022 sz s 0 eng d
020 $a 9783030896607 $q (electronic bk.)
020 $a 9783030896591 $q (paper)
024 7 $a 10.1007/978-3-030-89660-7 $2 doi
035 $a 978-3-030-89660-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA252.3 $b .P46 2022
072 7 $a PBG $2 bicssc
072 7 $a MAT014000 $2 bisacsh
072 7 $a PBG $2 thema
082 0 4 $a 512.482 $2 23
090 $a QA252.3 $b .P411 2022
100 1 $a Penkov, Ivan. $3 1566156
245 1 0 $a Classical lie algebras at infinity $h [electronic resource] / $c by Ivan Penkov, Crystal Hoyt.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xiii, 239 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a 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.
520 $a Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
650 0 $a Lie algebras. $3 526115
650 0 $a Infinite. $3 524340
650 1 4 $a Topological Groups and Lie Groups. $3 3593340
650 2 4 $a Algebra. $3 516203
700 1 $a Hoyt, Crystal. $3 3593339
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 1535313
856 4 0 $u https://doi.org/10.1007/978-3-030-89660-7
950 $a Mathematics and Statistics (SpringerNature-11649)