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Articles 1 - 3 of 3
Full-Text Articles in Algebra
Lecture 03: Hierarchically Low Rank Methods And Applications, David Keyes
Lecture 03: Hierarchically Low Rank Methods And Applications, David Keyes
Mathematical Sciences Spring Lecture Series
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the …
Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman
Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman
Mathematical Sciences Spring Lecture Series
Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.
On Leibniz Cohomology, Jorg Feldvoss, Friedrich Wagemann
On Leibniz Cohomology, Jorg Feldvoss, Friedrich Wagemann
University Faculty and Staff Publications
In this paper we prove the Leibniz analogue of Whitehead's vanishing theorem for the Chevalley-Eilenberg cohomology of Lie algebras. As a consequence, we obtain the second Whitehead lemma for Leibniz algebras. Moreover, we compute the cohomology of several Leibniz algebras with ad joint or irreducible coefficients. Our main tool is a Leibniz analogue of the Hochschild-Serre spectral sequence, which is an extension of the dual of a spectral sequence of Pirashvili for Leibniz homology from symmetric bimodules to arbitrary bimodules.