Results 61 to 70 of about 57,089 (167)
Publications of the Research Institute for Mathematical Sciences, 1975 Let M be a smooth manifold, and 2l(M) the Lie algebra of all smooth vector fields on M. Assume that M admits a volume form T, a symplectic form CD or a contact form 9. Then we have natural Lie subalgebras of 2l(M) as 21T(M), 2l;(M), 9IW(M), 2l;o(M), 210(M) (see §1.1). These Lie algebras including 2l(M) itself are called of classical type.
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A note on relative Gelfand–Fuks cohomology of spheres
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We study the Gelfand–Fuks cohomology of smooth vector fields on Sd$\mathbb {S}^d$ relative to SO(d+1)$\mathrm{SO}(d+1)$ following a method of Haefliger that uses tools from rational homotopy theory. In particular, we show that H∗(BSO(4);R)$H^*(\mathrm{B}\mathrm{SO}(4);\mathbb {R})$ injects into the relative Gelfand–Fuks cohomology which ...
Nils Prigge
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, 2023 This paper exhibits fundamental structure underlying Lie algebra homology with coefficients in tensor products of the adjoint representation, mostly focusing upon the case of free Lie algebras. The main result yields a DG category that is constructed from the PROP associated to the Lie operad.
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Representations up to homotopy of Lie algebroids [PDF]
, 2017 We introduce and study the notion of representation up to homotopy of a Lie algebroid, paying special attention to examples. We use representations up to homotopy to define the adjoint representation of a Lie algebroid and show that the resulting ...
Abad, Camilo Arias, Crainic, Marius
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Inonu-Wigner Contractions of Kac-Moody Algebras
, 1992 We discuss In\"on\"u-Wigner contractions of affine Kac-Moody algebras. We show that the Sugawara construction for the contracted affine algebra exists only for a fixed value of the level $k$, which is determined in terms of the dimension of the ...
Majumdar, Parthasarathi
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Polymatroidal tilings and the Chow class of linked projective spaces
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract Linked projective spaces are quiver Grassmannians of constant dimension one of certain quiver representations, called linked nets, over certain quivers, called Zn$\mathbb {Z}^n$‐quivers. They were recently introduced as a tool for describing schematic limits of families of divisors.
Felipe de Leon, Eduardo Esteves
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, 2000 This paper deals with the striking fact that there is an essentially canonical path from the $i$-th Lie algebra cohomology cocycle, $i=1,2,... l$, of a simple compact Lie algebra $\g$ of rank $l$ to the definition of its primitive Casimir operators $C ...
A. J. Macfarlane +10 more
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Which singular tangent bundles are isomorphic?
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Logarithmic and b$ b$‐tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these modified bundles resolve singularities by reframing singular vector fields as well‐behaved sections of these singular bundles.
Eva Miranda, Pablo Nicolás
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Semi-direct products of Lie algebras and their invariants
, 2007 The goal of this paper is to extend the standard invariant-theoretic design, well-developed in the reductive case, to the setting of representation of certain non-reductive groups. This concerns the following notions and results: the existence of generic
Panyushev, Dmitri I.
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Annalen der Physik, Volume 538, Issue 4, April 2026.ABSTRACT Quantum Mechanics (QM) and Climate Science (CS) confront the epistemic problem of inferring an unobservable state from incomplete, indirect, and context‐dependent measurements. Although their physics differ profoundly (non‐commutative algebra vs.
Gerrit Lohmann
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