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

切換: 標籤 | MARC模式 | ISBD

New Perspectives on Folding Affine L...

Coelho, Terence,

FindBook

Google Book

Amazon

博客來

New Perspectives on Folding Affine Lie Algebras by Dynkin Diagram Automorphisms /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	New Perspectives on Folding Affine Lie Algebras by Dynkin Diagram Automorphisms // Terence Coelho.
作者:	Coelho, Terence,
面頁冊數:	1 electronic resource (228 pages)
附註:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31933050
ISBN:	9798288805202

New Perspectives on Folding Affine Lie Algebras by Dynkin Diagram Automorphisms /
Coelho, Terence,

New Perspectives on Folding Affine Lie Algebras by Dynkin Diagram Automorphisms /Terence Coelho. - 1 electronic resource (228 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

Given a simply-laced aﬃne Lie algebra g(A) with aﬃne root system Φ and an automorphism σ of its Dynkin diagram that fixes the adjoined node, it is well-known that one can lift σ in various ways to g(A) such that the fixed-point subalgebra is a non-simply-laced twisted or untwisted aﬃne Lie algebra. Such automorphisms, which we call type-one, are easy to study using the realization of g(A) as a central extension of a loop algebra, with a derivation adjoined. If σ is not type-one, however, the liftings of σ to g(A) are much harder to study and the first results concerning their fixed-point sub-algebras were only recently uncovered by S.-Q. Liu, C.-Z. Wu, Y. Zhang, and X. Zhou. In this thesis, we provide a new realization of the simply-laced aﬃne Lie algebras that makes these liftings easier to study, which enables us to prove more about these fixed-point subalgebras. For instance, we prove that in most cases for which σ is not type-one and σ belongs to a certain family of liftings of σ to g(A), the fixed-point subalgebra may be expressed as the sum of a Heisenberg Lie algebra and a non-simply-laced aﬃne Lie algebra whose derived subalgebra commutes with the Heisenberg Lie algebra. We also provide an extension of some of these results to the setting of simply-laced Kac-Moody Lie algebras, extending an unpublished fact known to J. Fuchs, C. Schweigert, and A.N.Schellekens. This generalization will be motivated by the geometry of "folding" the root system of a simply-laced Kac-Moody Lie algebra by a Dynkin diagram automorphism.

English

ISBN: 9798288805202Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Affine Lie algebra

New Perspectives on Folding Affine Lie Algebras by Dynkin Diagram Automorphisms /
LDR:03028nmm a22004213i 4500 001 2433422
005 20250825062329.5
006 m o d
007 cr|nu||||||||
008 261011s2025 miu||||||m |||||||eng d
020 $a 9798288805202
035 $a (MiAaPQD)AAI31933050
035 $a AAI31933050
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Coelho, Terence, $e author. $3 3823027
245 1 0 $a New Perspectives on Folding Affine Lie Algebras by Dynkin Diagram Automorphisms / $c Terence Coelho.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (228 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
500 $a Advisors: Lepowsky, James Committee members: Carbone, Lisa; Sahi, Siddhartha; Ion, Bogdan.
502 $b Ph.D. $c Rutgers The State University of New Jersey, School of Graduate Studies $d 2025.
520 $a Given a simply-laced aﬃne Lie algebra g(A) with aﬃne root system Φ and an automorphism σ of its Dynkin diagram that fixes the adjoined node, it is well-known that one can lift σ in various ways to g(A) such that the fixed-point subalgebra is a non-simply-laced twisted or untwisted aﬃne Lie algebra. Such automorphisms, which we call type-one, are easy to study using the realization of g(A) as a central extension of a loop algebra, with a derivation adjoined. If σ is not type-one, however, the liftings of σ to g(A) are much harder to study and the first results concerning their fixed-point sub-algebras were only recently uncovered by S.-Q. Liu, C.-Z. Wu, Y. Zhang, and X. Zhou. In this thesis, we provide a new realization of the simply-laced aﬃne Lie algebras that makes these liftings easier to study, which enables us to prove more about these fixed-point subalgebras. For instance, we prove that in most cases for which σ is not type-one and σ belongs to a certain family of liftings of σ to g(A), the fixed-point subalgebra may be expressed as the sum of a Heisenberg Lie algebra and a non-simply-laced aﬃne Lie algebra whose derived subalgebra commutes with the Heisenberg Lie algebra. We also provide an extension of some of these results to the setting of simply-laced Kac-Moody Lie algebras, extending an unpublished fact known to J. Fuchs, C. Schweigert, and A.N.Schellekens. This generalization will be motivated by the geometry of "folding" the root system of a simply-laced Kac-Moody Lie algebra by a Dynkin diagram automorphism.
546 $a English
590 $a School code: 0190
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Affine Lie algebra
653 $a Dynkin diagram
653 $a Automorphism
653 $a Fixed-point subalgebras
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a Rutgers The State University of New Jersey, School of Graduate Studies. $b Mathematics. $e degree granting institution. $3 3823021
720 1 $a Lepowsky, James $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-01B.
790 $a 0190
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31933050