and their Lie algebras (tangent vectors near the identity) may be thought of as infinitesimal symmetry motions. Thus Lie algebras and their representations are used extensively in physics, notably in ...

This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a ...

This chapter is devoted to studying some concepts that will be extensively used in the last chapters, namely the cohomology of Lie algebras with values in a vector space, the Whitehead lemmas and Lie ...

Dr. Christine Uhl, associate professor of Mathematics, recently had two peer-reviewed articles published. Her work “Automorphisms of quantum polynomial rings and Drinfeld Hecke algebras,” coauthored ...

A simple implementation of the L-conv layer in PyTorch (>=1.8) can be found in src/lconv.py. The L-conv layer acts similar to a graph convlutional layer (GCN), so prepare your input in a similar ...

Abstract: We define a category of bounded modules for the full toroidal Lie algebra, classify irreducible modules in this category, and give their explicit vertex operator realizations. Using the ...

time‐varying systems and using an explicit representation for the solution of such systems in terms of a Lie algebra associated with the system. In the case of nilpotent Lie algebras we use a Lyapunov ...

Several fields of mathematics have developed in total isolation, using their own "undecipherable" coded languages. In a new ...

Several fields of mathematics have developed in total isolation, using their own 'undecipherable' coded languages. Mathematicians now present 'big algebras,' a two-way mathematical 'dictionary' ...

If you need open-heart surgery, as I do, the best person to perform it is a plumber. Who also happens to be a cardiovascular ...

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector ...