-duality and exceptional generalized geometry through symmetries of dg-manifolds

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• 作者：Ernesto Lupercio^a ; ^{lupercio@math.cinvestav.mx" class="auth_mail} ; ^{e_lupercio@hotmail.com" class="auth_mail} ; Camilo Rengifo^b ; ¹ ; ^{cam-reng@uniandes.edu.co" class="auth_mail} ; Bernardo Uribe^c ; ^{buribe@gmail.com" class="auth_mail}
• 关键词：primary ; 53D18 ; 53D17 ; secondary ; 55R65 ; 57R22
• 刊名：Journal of Geometry and Physics
• 出版年：September 2014
• 年：2014
• 卷：83
• 期：Complete
• 页码：82-98
• 全文大小：476 K

文摘

We study dg-manifolds which are R[2]$\mathbb{R}\left[2\right]$-bundles over R[1]$\mathbb{R}\left[1\right]$-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept of T$T$-dual dg-manifolds. Within this framework, we construct the T$T$-duality map as a degree −1 map between the cohomologies of the T$T$-dual dg-manifolds and we show an explicit isomorphism between the differential graded algebra of the symmetries of the 55f529a9b4bcc09b91a8c103b1c8" title="Click to view the MathML source">T$T$-dual dg-manifolds. We, furthermore, show how the algebraic structure underlying B_n$B_n$ generalized geometry could be recovered as derived dg-Leibniz algebra of the fixed points of the T$T$-dual automorphism acting on the symmetries of a self T$T$-dual dg-manifold, and we show how other types of algebraic structures underlying exceptional generalized geometry could be obtained as derived symmetries of certain dg-manifolds.