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Nondegenerate cohomology pairing for transitive Lie algebroids, characterization

Jan Kubarski, Alexandr Mishchenko (2004)

Open Mathematics

The Evens-Lu-Weinstein representation (Q A, D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q Aor, Dor) by tensoring by orientation flat line bundle, Q Aor=QA⊗or (M) and D or=D⊗∂Aor. It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q Aor, Dor) is the unique (up to isomorphy) line representation for which the top group of...

Non-degenerescence of some spectral sequences

K. S. Sarkaria (1984)

Annales de l'institut Fourier

Each Lie algebra ℱ of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold M définies, in a natural way, a spectral sequence E k ( ℱ ) which converges to the de Rham cohomology of M in a finite number of steps. We prove e.g. that for all k ≥ 0 there exists a foliated compact manifold with E k ( ℱ ) infinite dimensional.

Non-weight modules over the super Schrödinger algebra

Xinyue Wang, Liangyun Chen, Yao Ma (2024)

Czechoslovak Mathematical Journal

We construct a family of non-weight modules which are free U ( 𝔥 ) -modules of rank 2 over the N = 1 super Schrödinger algebra in ( 1 + 1 ) -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free U ( 𝔥 ) -modules of rank 2 over 𝔬𝔰𝔭 ( 1 | 2 ) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

Fιndιk, Şehmus (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Lm,c be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism φ of Lm,c is called normal if φ(I) = I for every ideal I of the algebra Lm,c. Such automorphisms form a normal subgroup N(Lm,c) of Aut (Lm,c) containing the group of inner automorphisms. We describe the group of normal automorphisms of Lm,c and the quotient group of Aut (Lm,c) modulo N(Lm,c).

Note on analytic Moufang loops

Eugen Paal (2004)

Commentationes Mathematicae Universitatis Carolinae

It is explicitly shown how the Lie algebras can be associated with the analytic Moufang loops. The resulting Lie algebra commutation relations are well known from the theory of alternative algebras.

Novikov superalgebras with A 0 = A 1 A 1

Fuhai Zhu, Zhiqi Chen (2010)

Czechoslovak Mathematical Journal

Novikov superalgebras are related to quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play a fundamental role in completely integrable systems. In this note we show that the Novikov superalgebras with A 0 = A 1 A 1 and dim A 1 = 2 are of type N and give a class of Novikov superalgebras of type S with A 0 = A 1 A 1 .

Noyau de Cauchy-Szegö d'un espace symétrique de type Cayley

Mohammed Chadli (1998)

Annales de l'institut Fourier

Dans cet article, en utilisant les algèbres de Jordan euclidiennes, nous étudions l’espace de Hardy H 2 ( Ξ ) d’un espace symétrique de type Cayley ℳ = G / H . Nous montrons que le noyau de Cauchy-Szegö de H 2 ( Ξ ) s’exprime comme somme d’une série faisant intervenir la fonction c de Harish-Chandra de l’espace symétrique riemannien D = G / K , la fonction c de l’espace symétrique c -dual 𝒩 de ℳ et les fonctions sphériques de l’espace symétrique ordonné 𝒩 . Nous établissons, dans le cas où la dimension de l’algèbre de Jordan associée...

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