Let be a Lie–Rinehart algebra such that L is S-projective and let U be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of U with values on a ...

Computer algebra is applied to biomedical computer vision. Specifically certain biomedical images resulting from a case of rhinocerebral mucormysocis in a diabetic boy are analyzed using techniques in computational geometry ...

In this article we present DiffAlg.m2, a differential algebra package for Macaulay2. It can perform the following operations: wedge products and exterior differentials of differential forms, contraction and Lie derivatives ...

We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants K of characteristic 0. Let x be a set of n differential variables, ...

We develop a theory of relative Kähler differentials for Lie algebras. The main result is that the functor of relative differentials is representable, and that the universal object which represents it behaves properly with ...

Nichols algebras, Hopf algebras in braided categories with distinguishedproperties, were discovered several times. They appeared for the first time in the thesis of W. Nichols [72], aimed to construct new examples of Hopf ...

A classical construction of Atiyah assigns to any (real or complex) Lie group G, manifold M and principal homogeneous G-space P over M, a Lie algebroid over M ([1]). The spirit behind our work is to put this work within ...

Let F be a differential field of characteristic 0, t=t1,…,tm a finite set of differential indeterminates over F and G⊂F〈t〉 a differential field extension of F, generated by nonconstant rational functions α1,…,αn of total ...

We give a complete description of the anti-involutions of the algebra DN of N X N-matrix differential operators on the circle, preserving the principal ℤ gradation. We obtain, up to conjugation, two families σ±,m with ...

We prove an effective integrability criterion for differential-algebraic Pfaffian systems leading to a decision method of consistency with a triple exponential complexity bound. As a byproduct, we obtain an upper bound for ...