Notes for a course, held in the Biebrza Marshes, Poland, May 6–10, 2010, on Frobenius categories of finite groups of Lie type.

Abstract We make some considerations and remarks on D = 11 supergravity its integral form. start from the geometrical formulation of by means form technique we provide a superspace action that reproduces (at quadratic level) recent in pure spinor framework. also Chevalley-Eilenberg cocycles their Hodge duals.

The original Loday–Quillen–Tsygan Theorem (LQT) is proven by Loday and Quillen [13] and independently by Tsygan [20]. It states that the ordinary Lie homology (here referred as Chevalley–Eilenberg–Lie homology) of the Lie algebra of the infinite matrices gl(A) over an unital associative algebra A is generated by the cyclic homology of A as an exterior algebra. Although Lie algebras have been st...