scholarly journals Homotopy Poisson algebras, Maurer–Cartan elements and Dirac structures of CLWX 2-algebroids

2021 ◽  
Author(s):  
Jiefeng Liu ◽  
Yunhe Sheng
Keyword(s):  
Poisson Algebras ◽  
Dirac Structures

scholarly journals Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Grgur Šimunić
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Target Space ◽  
Two Dimensional ◽  
Courant Algebroids ◽  
Dirac Structures ◽  
Courant Algebroid ◽  
Abelian Case ◽  
Jacobi Manifolds ◽  
Jacobi Structure

Abstract We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the Abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-Abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.

scholarly journals Poisson algebras via model theory and differential-algebraic geometry

2017 ◽  
Vol 19 (7) ◽  
pp. 2019-2049 ◽  
Author(s):  
Jason Bell ◽  
Stéphane Launois ◽  
Omar León Sánchez ◽  
Rahim Moosa
Keyword(s):  
Algebraic Geometry ◽  
Model Theory ◽  
Poisson Algebras

Kähler–Poisson algebras

2019 ◽  
Vol 136 ◽  
pp. 156-172 ◽  
Author(s):  
Joakim Arnlind ◽  
Ahmed Al-Shujary
Keyword(s):  
Poisson Algebras
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