Search

Start Over Subject Lie group

1. On some cohomological properties of the Lie algebra of Euclidean motions

Creator:
Bakšová, Marta and Dekrét, Anton
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Lie group, Lie algebra, dual space, twist; wrench, and cohomology
Language:
English
Description:
The external derivative d on differential manifolds inspires graded operators on complexes of spaces Λr g ∗ , Λr g ∗ ⊗ g, Λr g ∗ ⊗ g ∗ stated by g ∗ dual to a Lie algebra g. Cohomological properties of these operators are studied in the case of the Lie algebra g = se(3) of the Lie group of Euclidean motions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The general rigidity result for bundles of A-covelocities and A-jets

Creator:
Jiří Tomáš
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, r-jet, bundle functor, Weil functor, Lie group, jet group, B-admissible A-velocity, 13, and 51
Language:
English
Description:
Let M be an m-dimensional manifold and A = Dr k/I = R⊕NA a Weil algebra of height r. We prove that any A-covelocity TA x f ∈ TA x M, x ∈ M is determined by its values over arbitrary max{widthA,m} regular and under the first jet projection linearly independent elements of TA x M. Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result TA M ≃ T r M without coordinate computations, which improves and generalizes the partial result obtained in Tomáš (2009) from m > k to all cases of m. We also introduce the space JA(M,N) of A-jets and prove its rigidity in the sense of its coincidence with the classical jet space Jr(M,N)., Jiří Tomáš., and Seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public