Linear quotients

The goal of this note is to study graded ideals with linear free resolution and linear quotients in the exterior algebra. We use an extension of the notion of linear quotients, namely componentwise linear quotients, to give another proof of the well-known result that an ideal with linear quotients is componentwise linear.

12p vihermes2711 01-10-2019 10 0   Download

We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold. 1. Introduction The space of smooth first order linear differential operators on Rn that preserve harmonic functions is closed under Lie bracket. For n ≥ 3, it is finitedimensional (of dimension (n2 + 3n + 4)/2). Its commutator subalgebra is isomorphic to so(n + 1, 1), the Lie algebra of conformal motions of Rn .

22p noel_noel 17-01-2013 46 6   Download

Algebra is used by virtually all mathematicians, be they analysts, combinatorists, com- puter scientists, geometers, logicians, number theorists, or topologists. Nowadays, ev- eryone agrees that some knowledge of linear algebra, groups, and commutative rings is necessary, and these topics are introduced in undergraduate courses. We continue their study.

0p tiramisu0908 30-10-2012 81 12   Download