31 research outputs found
Universal Central Extensions of Gauge Algebras and Groups
We show that the canonical central extension of the group of sections of a
Lie group bundle over a compact manifold, constructed in [NW09], is universal.
In doing so, we prove universality of the corresponding central extension of
Lie algebras in a slightly more general setting.Comment: 9 pages, LaTeX. Changes w.r.t. version 2: minor changes (final
version). To appear in J. Reine Angew. Mat
Toric rings, inseparability and rigidity
This article provides the basic algebraic background on infinitesimal
deformations and presents the proof of the well-known fact that the non-trivial
infinitesimal deformations of a -algebra are parameterized by the
elements of cotangent module of . In this article we focus on
deformations of toric rings, and give an explicit description of in
the case that is a toric ring.
In particular, we are interested in unobstructed deformations which preserve
the toric structure. Such deformations we call separations. Toric rings which
do not admit any separation are called inseparable. We apply the theory to the
edge ring of a finite graph. The coordinate ring of a convex polyomino may be
viewed as the edge ring of a special class of bipartite graphs. It is shown
that the coordinate ring of any convex polyomino is inseparable. We introduce
the concept of semi-rigidity, and give a combinatorial description of the
graphs whose edge ring is semi-rigid. The results are applied to show that for
, is not rigid while for , is
rigid. Here is the complete bipartite graph with one
edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and
Applications>> 2018, Springer International Publishing AG, part of Springer
Natur
Combinatorics and Clifford Analysis
none2I. Sabadini; F. SommenSabadini, IRENE MARIA; F., Somme