We provide a systematic approach to obtain formulas for characters and Kostant u-homology groups of the oscillator modules of the finite dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for infinite dimensional Lie algebras. Specializing these Lie superalgebras to Lie algebras, we recover, in a new way, formulas for Kostant homology groups of unitarizable highes...

We construct a spectral sequence converging to the homology of ordered configuration spaces product parallelizable manifolds. To identify second page this sequence, we introduce version Boardman--Vogt tensor for linear operadic modules, purely algebraic operation. Using rational formality little cubes operads, show that our collapses in characteristic zero.

All rings in this paper are commutative and Noetherian. If R is a ring and I ⊂ R is an ideal, cd(R, I) denotes the cohomological dimension of I in R, i.e. the largest integer i such that the i-th local cohomology module H i I(M) doesn’t vanish for some R-module M . For the purposes of this introduction R is a complete equicharacteristic regular local d-dimensional ring with a separably closed r...

Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the prob...

In this paper we study local cohomology of finitely generated bigraded modules over a standard bigraded ring with respect to the irrelevant bigraded ideals and establish a duality theorem. Several applications are considered.

The quantum Euclidean spheres, S q , are (noncommutative) homogeneous spaces of quantum orthogonal groups, SOq(N). The ∗-algebra A(S q ) of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and ...

Cells can switch the functional states of extracellular matrix proteins by stretching them while exerting mechanical force. Using steered molecular dynamics, we investigated how the mechanical stability of FnIII modules from the cell adhesion protein fibronectin is affected by natural variations in their amino acid sequences. Despite remarkably similar tertiary structures, FnIII modules share l...

Viral structural genomic projects aim at unveiling the function of unknown viral proteins by employing high-throughput approaches to determine their 3D structure and to identify their function through fold-homology studies. The 'viral enzyme module localization' (VaZyMolO) tool has been developed, which aims at defining viral protein modules that might be expressed in a soluble and functionally...