Results 1 to 10 of about 1,933,260 (170)
From Lie algebras to Lie groups within synthetic differential geometry: Weil sprouts of Lie's third fundamental theorem [PDF]
Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of in nite-dimensional Lie groups how to construct a Lie group with a given Lie algebra as its Lie algebra or whether there exists such a Lie group at all.
Nishimura, Hirokazu
core +2 more sources
Special symplectic Lie groups and hypersymplectic Lie groups [PDF]
A special symplectic Lie group is a triple $(G,\omega,\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure $\nabla$.
A. Andrada+32 more
core +1 more source
Character groups of Hopf algebras as infinite-dimensional Lie groups [PDF]
In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we construct an infinite-dimensional Lie group structure on the character group with values in ...
Bogfjellmo, Geir+2 more
core +3 more sources
An Invitation to Higher Gauge Theory [PDF]
In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'.
A. Ashtekar+58 more
core +5 more sources
Categorified central extensions, \'etale Lie 2-groups and Lie's Third Theorem for locally exponential Lie algebras [PDF]
Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie ...
Agore+63 more
core +2 more sources
The path group construction of Lie group extensions
We present an explicit realization of abelian extensions of infinite dimensional Lie groups using abelian extensions of path groups, by generalizing Mickelsson's approach to loop groups and the approach of Losev-Moore-Nekrasov-Shatashvili to current ...
Vizman, Cornelia
core +2 more sources
Strictification of etale stacky Lie groups
We define stacky Lie groups to be group objects in the 2-category of differentiable stacks. We show that every connected and etale stacky Lie group is equivalent to a crossed module of the form (H,G) where H is the fundamental group of the given stacky ...
Baez+7 more
core +1 more source
Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories [PDF]
Let G be a Lie group which is the union of an ascending sequence of Lie groups G_n (all of which may be infinite-dimensional). We study the question when G is the direct limit of the G_n's in the category of Lie groups, topological groups, smooth ...
Außenhofer+51 more
core +5 more sources
Making tau amyloid models in vitro: a crucial and underestimated challenge
This review highlights the challenges of producing in vitro amyloid assemblies of the tau protein. We review how accurately the existing protocols mimic tau deposits found in the brain of patients affected with tauopathies. We discuss the important properties that should be considered when forming amyloids and the benchmarks that should be used to ...
Julien Broc, Clara Piersson, Yann Fichou
wiley +1 more source
From Loop Groups to 2-Groups [PDF]
We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism ...
Baez, John C.+3 more
core +2 more sources