Abstract:
In this work we study decompositions G=G′G″ of reductive Lie groups G into the product of Lie subgroups G′ and G″. Such decompositions are fully described in case G′ and G″ are reductive in G, or G is simple and G′ and G″ are maximal. The results are applied to the classification of complex homogeneous spaces.
Bibliography: 21 titles.
This publication is cited in the following 37 articles:
Dmitri I. Panyushev, “Projections of Nilpotent Orbits in a Simple Lie Algebra and Shared Orbits”, Algebr Represent Theor, 2025
V. V. Gorbatsevich, “O razlozheniyakh i tranzitivnykh deistviyakh nilpotentnykh grupp Li”, Izv. vuzov. Matem., 2024, no. 4, 3–14
V. V. Gorbatsevich, “On Decompositions and Transitive Actions of Nilpotent Lie Groups”, Russ Math., 68:4 (2024), 1
Maciej Bocheński, Aleksy Tralle, “Standard Compact Clifford-Klein Forms and Lie Algebra Decompositions”, Transformation Groups, 2024
Dietrich Burde, Wolfgang Alexander Moens, “Semisimple decompositions of Lie algebras and prehomogeneous modules”, Journal of Algebra, 604 (2022), 664
Dietrich Burde, Karel Dekimpe, Mina Monadjem, “Rigidity results for Lie algebras admitting a post-Lie algebra structure”, Int. J. Algebra Comput., 32:08 (2022), 1495
V. Gubarev, “Unital decompositions of the matrix algebra of order three”, Communications in Algebra, 49:11 (2021), 4980
D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, L. S. Kazarin, D. A. Leites, A. M. Lukatskii, A. N. Shchetinin, “Arkadii L'vovich Onishchik (obituary)”, Russian Math. Surveys, 75:4 (2020), 765–777
GABRIEL BĂDIŢOIU, “CLASSIFICATION OF HOMOGENEOUS EINSTEIN METRICS ON PSEUDO-HYPERBOLIC SPACES”, Transformation Groups, 25:2 (2020), 335
Dietrich Burde, Vsevolod Gubarev, “Decompositions of algebras and post-associative algebra structures”, Int. J. Algebra Comput., 30:03 (2020), 451
Konrad Lompert, Andriy Panasyuk, “Invariant Nijenhuis Tensors and Integrable Geodesic Flows”, SIGMA, 15 (2019), 056, 30 pp.
FRIEDRICH KNOP, BERNHARD KRÖTZ, TOBIAS PECHER, HENRIK SCHLICHTKRULL, “CLASSIFICATION OF REDUCTIVE REAL SPHERICAL PAIRS I. THE SIMPLE CASE”, Transformation Groups, 24:1 (2019), 67
Dietrich Burde, Vsevolod Gubarev, “Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras”, Communications in Algebra, 47:5 (2019), 2280
Henrik Schlichtkrull, Peter E. Trapa, David A. Vogan, “Laplacians on spheres”, São Paulo J. Math. Sci., 12:2 (2018), 295
D.A.. Towers, “Supplements to Maximal Subalgebras of Lie Algebras”, Communications in Algebra, 41:10 (2013), 3848
Dmitri Akhiezer, Progress in Mathematics, 306, Lie Groups: Structure, Actions, and Representations, 2013, 1
Anisimov A., “Spherical Subgroups and Double Coset Varieties”, J. Lie Theory, 22:2 (2012), 505–522
V. V. Gorbatsevich, “On Diverse Forms of Homogeneity of Lie Algebras”, Math. Notes, 88:2 (2010), 165–176
V. V. Gorbatsevich, “Compact Homogeneous Spaces and Their Generalizations”, Journal of Mathematical Sciences, 153:6 (2008), 763–798
M. V. Tvalavadze, “Simple Decompositions of Simple Special Jordan Superalgebras”, Comm. in Algebra, 35:6 (2007), 2008
Citation in format AMSBIB
Contact us: