TY - JOUR
T1 - G-Algebroids
T2 - A Unified Framework for Exceptional and Generalised Geometry, and Poisson–Lie Duality
AU - Bugden, Mark
AU - Hulík, Ondřej
AU - Valach, Fridrich
AU - Waldram, Daniel
N1 - Funding Information:
The authors would like to thank Florian Naef, Jan Slovák, Charles Strickland‐Constable, and Pavol Ševera for helpful discussions and comments. The authors would also like to acknowledge the Higher Structures and Field Theory programme at the Erwin Schrödinger Institute in Vienna, Austria, in September 2020, where part of the research was carried out. Research of M.B. was supported by the GAČR Grant EXPRO 19‐28628X. Research of O.H. was supported by the GAČR Grant EXPRO 20‐25775X. F.V. was supported by the Early Postdoc Mobility grant P2GEP2_188247 of the Swiss National Science Foundation. D.W. was supported in part by the STFC Consolidated Grants ST/P000762/1 and ST/T000791/1 and the EPSRC New Horizons Grant EP/V049089/1.
Publisher Copyright:
© 2021 The Authors. Fortschritte der Physik published by Wiley-VCH GmbH
PY - 2021/5
Y1 - 2021/5
N2 - We introduce the notion of (Formula presented.) -algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in (Formula presented.) exceptional generalised geometry for (Formula presented.). Focusing on the exceptional case, we prove a classification of “exact” algebroids and translate the related classification of Leibniz parallelisable spaces into a tractable algebraic problem. After discussing the general notion of Poisson–Lie duality, we show that the Poisson–Lie U-duality is compatible with the equations of motion of supergravity.
AB - We introduce the notion of (Formula presented.) -algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in (Formula presented.) exceptional generalised geometry for (Formula presented.). Focusing on the exceptional case, we prove a classification of “exact” algebroids and translate the related classification of Leibniz parallelisable spaces into a tractable algebraic problem. After discussing the general notion of Poisson–Lie duality, we show that the Poisson–Lie U-duality is compatible with the equations of motion of supergravity.
UR - http://www.scopus.com/inward/record.url?scp=85105135367&partnerID=8YFLogxK
U2 - 10.1002/prop.202100028
DO - 10.1002/prop.202100028
M3 - Article
AN - SCOPUS:85105135367
SN - 0015-8208
VL - 69
JO - Fortschritte der Physik
JF - Fortschritte der Physik
IS - 4-5
M1 - 2100028
ER -