Related papers: Exterior algebra resolutions arising from homogene…
In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…
We consider principal bundles over homogeneous spaces G/P, where P is a parabolic subgroup of a semisimple and simply connected complex linear algebraic group G. We prove that a holomorphic principal H--bundle, where H is a complex…
Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra $\Lambda$ is left or right glued if and only if $\Lambda$ is…
For nonlinear differential-algebraic equations (DAEs), we define two kinds of equivalences, namely, the external and internal equivalence. Roughly speaking, the word "external" means that we consider a DAE (locally) everywhere and…
Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We consider square matrices over $\mathbb{C}$ satisfying an identity relating their eigenvalues and the corresponding eigenvectors re-proved and discussed by Denton, Parker, Tao and Zhang, called the eigenvector-eigenvalue identity. We…
We compute the Euler characteristics of tautological vector bundles and their exterior powers over the Quot schemes of curves. We give closed-form expressions over punctual Quot schemes in all genera. For higher rank quotients of a trivial…
We study the problem of computing the exterior modulus of a bounded quadrilateral. We reduce this problem to the numerical solution of the Dirichlet-Neumann problem for the Laplace equation. Several experimental results, with error…
The notion of an exterior differential system (on a manifold) has recently been extended to the setting of a Lie algebroid. Here, we further develop the theory and we present two versions of the Cartan-K\"ahler theorem in the case where the…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…
We know the multiplicity of the adjoint representation of a semisimple Lie algebra in its own exterior algebra, but how do its copies distribute themselves between the exterior powers? The answer (the graded multiplicity) is obtained with…
In the present article we work out a relative setup of generic structures on surface singularities. We fix an analytic type on a subgraph of a rational homology sphere resolution graph $\mathcal{T}$ and we choose a relatively generic normal…
We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety $V$ in terms of the geometric degree of $V$. We first analyze the case of curves, showing an explicit relation…
In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…
We present two families of exterior differential systems (EDS) for non-isometric embeddings of orthonormal frame bundles over Riemannian spaces of dimension q = 2, 3, 4, 5.... into orthonormal frame bundles over flat spaces of sufficiently…
In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…
Natural analogs of Lie brackets on affine bundles are studied, based on natural examples from differential geometry and analytical mechanics. In particular, a close relation to Lie algebroids and, by a sort of duality, to affine analogs of…
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
A Lie algebroid over a manifold is a vector bundle over that manifold whose properties are very similar to those of a tangent bundle. Its dual bundle has properties very similar to those of a cotangent bundle: in the graded algebra of…