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The Wonderful Compactification and t...

The University of Chicago.

The Wonderful Compactification and the Universal Centralizer.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	The Wonderful Compactification and the Universal Centralizer./
Author:	Balibanu, Ana Silvia.
Description:	1 online resource (54 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355077490

The Wonderful Compactification and the Universal Centralizer.
Balibanu, Ana Silvia.

The Wonderful Compactification and the Universal Centralizer. - 1 online resource (54 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis describes work of the author involving the geometry of the wonderful compactification of a complex semisimple algebraic group G of adjoint type. We consider the centralizer Ge in G of a regular nilpotent element e epsilon Lie(G), and we prove that its closure in the wonderful compactification is isomorphic to the Peterson variety. We generalize this result to show that the closure in the wonderful compactification of the centralizer Gx of any regular element x epsilon Lie(G) is isomorphic to the closure of a general Gx-orbit in the flag variety.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355077490Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

The Wonderful Compactification and the Universal Centralizer.
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008 190606s2017 xx obm 000 0 eng d
020 $a 9780355077490
035 $a (MiAaPQ)AAI10269824
035 $a (MiAaPQ)uchicago:13728
035 $a AAI10269824
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Balibanu, Ana Silvia. $3 1180696
245 1 4 $a The Wonderful Compactification and the Universal Centralizer.
264 0 $c 2017
300 $a 1 online resource (54 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: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
500 $a Adviser: Victor Ginzburg.
502 $a Thesis (Ph.D.) $c The University of Chicago $d 2017.
504 $a Includes bibliographical references
520 $a This thesis describes work of the author involving the geometry of the wonderful compactification of a complex semisimple algebraic group G of adjoint type. We consider the centralizer Ge in G of a regular nilpotent element e epsilon Lie(G), and we prove that its closure in the wonderful compactification is isomorphic to the Peterson variety. We generalize this result to show that the closure in the wonderful compactification of the centralizer Gx of any regular element x epsilon Lie(G) is isomorphic to the closure of a general Gx-orbit in the flag variety.
520 $a We then consider the family X¯ of all closures of such centralizers, parametrized by conjugacy classes of regular elements in Lie(G). This is a relative compactification of the universal centralizer X , which has a natural symplectic structure arising from a Hamiltonian reduction of the cotangent bundle of G . We prove that the symplectic structure on X extends to a log-symplectic Poisson structure on X¯, by realizing X¯ as a Hamiltonian reduction of the logarithmic cotangent bundle of the wonderful compactification.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Chicago. $b Mathematics. $3 1180611
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10269824 $z click for full text (PQDT)

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