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＜電子ブック＞
Groups, Invariants, Integrals, and Mathematical Physics : The Wisła 20-21 Winter School and Workshop / edited by Maria Ulan, Stanislav Hronek
(Tutorials, Schools, and Workshops in the Mathematical Sciences. ISSN:25220977)

版	1st ed. 2023.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2023
本文言語	英語
大きさ	XV, 251 p. 29 illus., 6 illus. in color : online resource
著者標目	Ulan, Maria editor Hronek, Stanislav editor SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Group theory LCSH:Topological groups LCSH:Lie groups LCSH:Differential equations LCSH:Algebra, Homological FREE:Mathematical Physics FREE:Group Theory and Generalizations FREE:Topological Groups and Lie Groups FREE:Differential Equations FREE:Category Theory, Homological Algebra
一般注記	Lychagin, V., Roop, M., Differential Invariants in Algebra -- Rubtsov, V., Suchánek, R., Lectures on Poisson Algebras -- Suchánek,R., Some Remarks on Multisymplectic and Variational Nature of Monge-Ampère Equations in Dimension Four -- Ruiz, A., Muriel, C., Generalized Solvable Structures Associated to Symmetry Algebras Isomorphic to $\mathfrak{gl}(2,\mathbb{R}) \ltimes \mathbb{R}$ -- Maksymenko, S., Nikitchenko, O., Fundamental Groupoids and Homotopy Types of Non-Compact Surfaces -- Barth, L. S., A Geometric Framework to Compare Classical Field Theories This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed HTTP:URL=https://doi.org/10.1007/978-3-031-25666-0

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