26,017 research outputs found
On central extensions of simple differential algebraic groups
We consider central extensions in
the category of linear differential algebraic groups. We show that if is
simple non-commutative and is unipotent with the differential type smaller
than that of , then such an extension splits. We also give a construction of
central extensions illustrating that the condition on differential types is
important for splitting. Our results imply that non-commutative almost simple
linear differential algebraic groups, introduced by Cassidy and Singer, are
simple.Comment: 13 page
A Wells type exact sequence for non-degenerate unitary solutions of the Yang--Baxter equation
Cycle sets are known to give non-degenerate unitary solutions of the
Yang--Baxter equation and linear cycle sets are enriched versions of these
algebraic systems. The paper explores the recently developed cohomology and
extension theory for linear cycle sets. We derive a four term exact sequence
relating 1-cocycles, second cohomology and certain groups of automorphisms
arising from central extensions of linear cycle sets. This is an analogue of a
similar exact sequence for group extensions known due to Wells. We also compare
the exact sequence for linear cycle sets with that for their underlying abelian
groups via the forgetful functor and discuss generalities on dynamical
2-cocycles.Comment: 18 pages, to appear in Homology Homotopy Application
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