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Algebraic Bol loops
(WALTER DE GRUYTER & CO, 2011)
In this paper, we study the category of algebraic Bol loops over an algebraically closed field of definition. On the one hand, we apply techniques from the theory of algebraic groups in order to prove structural theorems ...
On Demazure And Local Weyl Modules For Affine Hyperalgebras
(PACIFIC JOURNAL MATHEMATICSBERKELEY, 2015)
Torsors, reductive group schemes and extended affine Lie algebras
(American Mathematical Society, 2013-11)
We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction ...
ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES
(WORLD SCIENTIFIC PUBL CO PTE LTDSingapura, 2009)
We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. ...
Gravitation in terms of observables 2: the algebra of fundamental observables
(IOP Publishing, 2020)
In a previous paper, we showed how to use the techniques of the group of loops to formulate the loop approach to gravity proposed by Mandelstam in the 1960's. Those techniques allow to overcome some of the difficulties ...
Entropic order parameters for the phases of QFT
(Springer, 2021-04)
We propose entropic order parameters that capture the physics of generalized symmetries and phases in QFT’s. We do it through an analysis of simple properties (additivity and Haag duality) of the net of operator algebras ...
Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation
(2004-01-12)
Supersymmetry is formulated for integrable models based on the sl(2 1) loop algebra endowed with a principal gradation. The symmetry transformations which have half-integer grades generate supersymmetry. The sl(2 1) loop ...