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Deformations and the koherence

Markl, Martin (1994)

Proceedings of the Winter School "Geometry and Physics"

The cotangent cohomology of S. Lichtenbaum and M. Schlessinger [Trans. Am. Math. Soc. 128, 41-70 (1967; Zbl 0156.27201)] is known for its ability to control the deformation of the structure of a commutative algebra. Considering algebras in the wider sense to include coalgebras, bialgebras and similar algebraic structures such as the Drinfel’d algebras encountered in the theory of quantum groups, one can model such objects as models for an algebraic theory much in the sense of F. W. Lawvere [Proc....

Examples of quantum braided groups

Hlavatý, Ladislav (1994)

Proceedings of the Winter School "Geometry and Physics"

Summary: The author gives the defining relations of a new type of bialgebras that generalize both the quantum groups and braided groups as well as the quantum supergroups. The relations of the algebras are determined by a pair of matrices ( R , Z ) that solve a system of Yang-Baxter-type equations. The matrix coproduct and counit are of standard matrix form, however, the multiplication in the tensor product of the algebra is defined by virtue of the braiding map given by the matrix Z . Besides simple solutions...

Finite group actions on 2- dimensional CW-complexes

Dorabiala, Wojciech (1994)

Proceedings of the Winter School "Geometry and Physics"

Let X be a cell complex obtained by attaching a 2-cell to a finite bouquet of circles (for example, a closed surface). In terms of the combinatorial type of the attaching map, the paper gives conditions for the existence of a fixed point free (topological) homeomorphism of the complex X . Also, quotients of finite group actions on such complexes are considered as well as a condition under which the induced actions on cohomology are trivial.

Foliated groupoids

Lisiecki, Krzysztof (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The author defines a general notion of a foliated groupoid over a foliation with singularities, within the framework of a (known) general notion of a differentiable structure. Then, he generalizes the classical correspondence between the subalgebras of Lie algebras and the subgroups of the corresponding Lie groups for this type of pseudogroups.

Foreword

Bureš, J., Souček, V. (1990)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1987)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1996)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Slovák, Jan (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1994)

Proceedings of the Winter School "Geometry and Physics"

Foreword

Bureš, J., Souček, V. (1989)

Proceedings of the Winter School "Geometry and Physics"

General Nijenhuis tensor: an example of a secondary invariant

Studený, Václav (1996)

Proceedings of the Winter School "Geometry and Physics"

The author considers the Nijenhuis map assigning to two type (1,1) tensor fields α , β a mapping 〈 α , β 〉 : ( ξ , ζ ) ↦ [ α ( ξ ) , β ( ζ ) ] + α ∘ β ( [ ξ , ζ ] ) - α ( [ ξ , β ( ζ ) ] ) - β ( [ α ( ξ ) , ζ ) ] ) , where ξ , ζ are vector fields. Then 〈 α , β 〉 is a type (2,1) tensor field (Nijenhuis tensor) if and only if [ α , β ] = 0 . Considering a smooth manifold X with a smooth action of a Lie group, a secondary invariant may be defined as a mapping whose area of invariance is restricted to the inverse image of an invariant subset of X under another invariant mapping. The author recognizes a secondary invariant related to the...

Generalized Einstein manifolds

Formella, Stanisław (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] A manifold (M,g) is said to be generalized Einstein manifold if the following condition is satisfied ( ∇ X S ) ( Y , Z ) = σ ( X ) g ( Y , Z ) + ν ( Y ) g ( X , Z ) + ν ( Z ) g ( X , Y ) where S(X,Y) is the Ricci tensor of (M,g) and σ (X), ν (X) are certain ℓ -forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g( ψ (X), ψ (X)) ≠ 0 .

Currently displaying 21 – 40 of 125