The binary bracket of a Courant algebroid structure on (E,〈⋅,⋅〉) can be extended to n-ary Γ(E), yielding multi-Courant algebroid. These brackets form Poisson algebra and were defined, in an algebraic setting, by Keller Waldmann. We construct higher geometric version Keller-Waldmann define algebroids. As structures seen as degree 3 functions graded symplectic manifold 2, n≥3 that manifold.

A generalized Courant algebroid structure is defined on the direct sum bundle DE ⊕ JE, where DE and JE are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a structure is called an omni-Lie algebroid since it is reduced to the omni-Lie algebra introduced by A.Weinstein if the base manifold is a point. We prove that any Lie algebroid structure on E is characteri...

1. Even periodic ring theories and formal group laws 1 2. Formal groups 5 3. Geometry of formal groups 8 4. Heights of formal groups 12 5. Homology of Z× BU and related spaces 15 6. The Thom isomorphism 19 7. Elliptic spectra 24 8. The generalized Weierstrass equation 25 9. Modular forms 29 10. Elliptic curves and the group structure 30 11. Weierstrass parameters and Thom spectrum of ΩU(4) 33 1...

In this note a functorial approach to the integration problem of an LAgroupoid to a double Lie groupoid is discussed. To do that, we study the notions of fibered products in the categories of Lie groupoids and Lie algebroids, giving necessary and sufficient conditions for the existence of such. In particular, it turns out, that the fibered product of Lie algebroids along integrable morphisms is...

A Q-algebroid is a Lie superalgebroid equipped with a compatible homological vector field and is the infinitesimal object corresponding to a Q-groupoid. We associate to every Q-algebroid a double complex. As a special case, we define the BRST model of a Lie algebroid, which generalizes the BRST model for equivariant cohomology. We extend to this setting the Mathai-Quillen-Kalkman isomorphism of...