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]

, 2013
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]

, 2010
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, A. Andrada, A. Andrada, A. Diatta, A. Fino, A. Lichnerowicz, A.A. Balinskii, B.Y. Chu, C. Bartocci, C.M. Bai, C.M. Bai, C.M. Bai, Chengming Bai, D. Alekseevsky, D. Alekseevsky, D. Burde, D. Burde, H. Kamada, H. Ooguri, J.-H. Lu, J.-L. Loday, M. Takeuchi, M.L. Barberis, N.B. Boyom, N.B. Boyom, N.J. Hitchin, P. Libermann, R. Schafer, S. Kaneyuki, S. Majid, V. Chari, V.G. Drinfeld, Xiang Ni   +32 more
core   +1 more source

Character groups of Hopf algebras as infinite-dimensional Lie groups [PDF]

, 2015
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, Dahmen, Rafael, Schmeding, Alexander   +2 more
core   +3 more sources

An Invitation to Higher Gauge Theory [PDF]

, 2010
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, A. Baratin, A. Baratin, A. Pressley, A.J. Power, A.L. Carey, A.P. Balachandran, B. Eckmann, C. DeWitt-Morette, D.S. Freed, E. Witten, F. Girelli, F. Girelli, H. Pfeiffer, H. Weyl, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Baez, J. Elgueta, J. Lewandowski, J.-L. Brylinski, J.-L. Brylinski, J.-L. Brylinski, J.H.C. Whitehead, J.H.C. Whitehead, J.W. Barrett, John C. Baez, John Huerta, K. Gawedzki, K. Gawedzki, L. Breen, L. Breen, L. Castellani, L. Crane, L. Crane, L. Freidel, M. Johnson, M. Mackaay, M. Montesinos, M. Schlessinger, M.K. Murray, M.K. Murray, P. Aschieri, P. Aschieri, S. Mac Lane, S. Stolz, T. DeDonder, U. Schreiber, V. Guillemin, W. Fairbairn   +58 more
core   +5 more sources

Categorified central extensions, \'etale Lie 2-groups and Lie's Third Theorem for locally exponential Lie algebras [PDF]

, 2011
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, Baer, Baez, Baez, Baez, Baez, Baez, Blanco, Blohmann, Bourbaki, Bourgin, Breen, Brylinski, Brylinski, Cartan, Cartan, Christoph Wockel, Crainic, Douady, Eilenberg, Forrester-Barker, Glöckner, Glöckner, Glöckner, Henriques, Hofmann, Hofmann, Iglesias-Zemmour, Iglésias, Jacobson, Kiechle, Kriegl, Lang, Lempert, Loday, MacLane, Maier, Mickelsson, Murray, Nagy, Neeb, Neeb, Nikolaus, Nikolaus, Olver, Pflugfelder, Porst, Pradines, Pressley, Schommer-Pries, Schreiber, Smith, Stolz, Stolz, Tseng, Tuynman, van Est, van Est, van Est, Waldorf, Weinstein, Wockel, Wockel, Wockel   +63 more
core   +2 more sources

The path group construction of Lie group extensions

, 2008
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

, 2010
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, Blohmann, Chenchang Zhu, Friedlander, Giorgio Trentinaglia, MacLane, Tseng, Zhu   +7 more
core   +1 more source

Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories [PDF]

, 2006
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, Banaszczyk, Banyaga, Bertram, Bierstedt, Bochnak, Bourbaki, Bourbaki, Dierolf, Edamatsu, Floret, Frölicher, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Glöckner, Haller, Hansen, Helge Glöckner, Hewitt, Hirai, Hogbe-Nlend, Jarchow, Kamran, Kriegl, Leitenberger, Michael, Michor, Milnor, Natarajan, Natarajan, Neeb, Neeb, Neeb, Neeb, Pietsch, Pisanelli, Schaefer, Tatsuuma, Trèves, Yamasaki   +51 more
core   +5 more sources

Making tau amyloid models in vitro: a crucial and underestimated challenge

FEBS Letters, EarlyView.
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]

, 2005
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., Crans, Alissa S., Schreiber, Urs, Stevenson, Danny   +3 more
core   +2 more sources