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Two Applications of the Homotopy Transfer Theorem for Infinity-Algebras.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two Applications of the Homotopy Transfer Theorem for Infinity-Algebras./
Author:	Papayanov, Grigory.
Description:	1 online resource (110 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30487882click for full text (PQDT)
ISBN:	9798379586423

Two Applications of the Homotopy Transfer Theorem for Infinity-Algebras.
Papayanov, Grigory.

Two Applications of the Homotopy Transfer Theorem for Infinity-Algebras. - 1 online resource (110 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--Northwestern University, 2023.

Includes bibliographical references

In the first part of the thesis we, given a dg-Lie algebra g, a commutative dg-algebra A and a twisting cochain µ in A⊗g, we construct a map from the functor of curved deformations of g to the functor of curved deformations of the twisted tensor product A⊗µ g, which we call the precomposition map. As an application, we upgrade the noncommutative period map of Fedosov to a map of deformation functors. This allows one to reprove the results of Nest-Tsygan about classification of holomorphically symplectic quantizations as well as to write down a formula for the period map on the level of cohomology. In the second part of the thesis we prove that the cohomology algebra of a conilpotent Lie coalgebra is generated by H1 as an A∞-algebra.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379586423Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

A-infinity algebrasIndex Terms--Genre/Form:

542853
Electronic books.

Two Applications of the Homotopy Transfer Theorem for Infinity-Algebras.
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Tsygan, Boris.
502 $a Thesis (Ph.D.)--Northwestern University, 2023.
504 $a Includes bibliographical references
520 $a In the first part of the thesis we, given a dg-Lie algebra g, a commutative dg-algebra A and a twisting cochain µ in A⊗g, we construct a map from the functor of curved deformations of g to the functor of curved deformations of the twisted tensor product A⊗µ g, which we call the precomposition map. As an application, we upgrade the noncommutative period map of Fedosov to a map of deformation functors. This allows one to reprove the results of Nest-Tsygan about classification of holomorphically symplectic quantizations as well as to write down a formula for the period map on the level of cohomology. In the second part of the thesis we prove that the cohomology algebra of a conilpotent Lie coalgebra is generated by H1 as an A∞-algebra.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a A-infinity algebras
653 $a Deformation theory
653 $a L-infinity algebras
653 $a Lie coalgebra
653 $a Period map
653 $a Quantization
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 783688
710 2 $a Northwestern University. $b Mathematics. $3 1280008
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30487882 $z click for full text (PQDT)