A note on the symplectic geometry of semisimple groups

Hassan Azad; Indranil Biswas

doi:10.1016/j.bulsci.2009.02.002

A note on the symplectic geometry of semisimple groups

Hassan Azad, Indranil Biswas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Let K^C be the complexification of a compact connected Lie group K. Fixing a K-invariant inner product on Lie (K), the total space of T^* K is identified with K^C. We show that the Liouville symplectic form on T^* K is Kähler with respect to the complex structure of K^C.

Original language	English
Pages (from-to)	330-334
Number of pages	5
Journal	Bulletin des Sciences Mathematiques
Volume	133
Issue number	4
DOIs	https://doi.org/10.1016/j.bulsci.2009.02.002
State	Published - May 2009
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1016/j.bulsci.2009.02.002

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title = "A note on the symplectic geometry of semisimple groups",

abstract = "Let KC be the complexification of a compact connected Lie group K. Fixing a K-invariant inner product on Lie (K), the total space of T* K is identified with KC. We show that the Liouville symplectic form on T* K is K{\"a}hler with respect to the complex structure of KC.",

author = "Hassan Azad and Indranil Biswas",

year = "2009",

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doi = "10.1016/j.bulsci.2009.02.002",

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AU - Azad, Hassan

AU - Biswas, Indranil

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N2 - Let KC be the complexification of a compact connected Lie group K. Fixing a K-invariant inner product on Lie (K), the total space of T* K is identified with KC. We show that the Liouville symplectic form on T* K is Kähler with respect to the complex structure of KC.

AB - Let KC be the complexification of a compact connected Lie group K. Fixing a K-invariant inner product on Lie (K), the total space of T* K is identified with KC. We show that the Liouville symplectic form on T* K is Kähler with respect to the complex structure of KC.

UR - https://www.scopus.com/pages/publications/67349179038

U2 - 10.1016/j.bulsci.2009.02.002

DO - 10.1016/j.bulsci.2009.02.002

M3 - Article

AN - SCOPUS:67349179038

SN - 0007-4497

VL - 133

SP - 330

EP - 334

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

IS - 4

ER -

A note on the symplectic geometry of semisimple groups

Abstract

ASJC Scopus subject areas

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