Many interesting geometric structures can be defined by specifying a smooth subbundle V of the complexified tangent bundle of the underlying smooth manifold, subject to an integrability condition. Examples include foliations, complex structures, and CR structures. In general such structures are called involutive, or formally integrable, and their study has been the starting point of far-reachin...

In this paper we give a method which uses a nite number of di erentiations and linear operations to determine the Cartan structure of structurally transitive Lie pseudogroups from their in nitesimal de ning equations. These equations are the linearized form of the pseudogroup de ning system { the system of pdes whose solutions are the transformations belonging to the pseudogroup. In many applic...

Hyperoctahedral homology is the theory associated to hyperoctahedral crossed simplicial group. It defined for involutive algebras over a commutative ring using functor and bar construction of Fiedorowicz. The main result paper proves that related equivariant stable homotopy theory: discrete group odd order, algebra isomorphic fixed points under involution an infinite loop space built from class...

The GVW algorithm computes simultaneously Gröbner bases of a given ideal and the syzygy module generating set. In this work, we discuss an extension it to involutive bases. Pommaret play here special role in several respects. We distinguish between fully which determines for both semi-involutive version only ordinary basis. A prototype implementation developed algorithms Maple is described.

It is often inevitable to introduce an indefinite-metric space in quantum field theory, for example, which is explained for the sake of the manifestly covariant quantization of the electromagnetic field. We show two more evident mathematical reasons why such indefinite metric appears. The first idea is the replacement of involution on an algebra. For an algebra A with an involution † such that ...