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إعادة تعيين
110
نتائج ل
"Rajan, Amit"
صنف حسب:
Modular Classes of Lie Groupoid Representations up to Homotopy
بواسطة
Mehta, Rajan Amit
2015
We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein's ''The volume of a differentiable stack''. [ProQuest: [...] denotes formulae omitted.]
Journal Article
Frobenius objects in the category of spans
2021
We consider Frobenius objects in the category Span, where the objects are sets and the morphisms are isomorphism classes of spans of sets. We show that such structures are in correspondence with data that can be characterized in terms of simplicial sets. An interesting class of examples comes from groupoids. Our primary motivation is that Span can be viewed as a set-theoretic model for the symplectic category, and thus Frobenius objects in Span provide set-theoretic models for classical topological field theories. The paper includes an explanation of this relationship.
Paper
On Examples and Classification of Frobenius Objects in Rel
2022
We give some new examples of Frobenius objects in the category of sets and relations \\(\\textbf{Rel}\\). One example is a groupoid with a twisted counit. Another example is the set of conjugacy classes of a group. We also classify Frobenius objects in \\(\\textbf{Rel}\\) with two or three elements, and we compute the associated surface invariants using the partition functions of the corresponding TQFTs.
Paper
Courant cohomology, Cartan calculus, connections, curvature, characteristic classes
2020
We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan formula for the de Rham differential. This perspective allows us to develop the theory of Courant algebroid connections in a way that mirrors the classical theory of connections. Using a special class of connections, we construct secondary characteristic classes associated to any Courant algebroid.
Paper
Frobenius objects in the category of relations
2019
We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of relations are in correspondence with groupoids. As an additional example, we construct a Frobenius object in the category of relations whose elements are certain cohomology classes in a compact oriented Riemannian manifold.
Paper
Hypokalemic Periodic Paralysis: A Rare Case of a Descending Flaccid Paralysis
بواسطة
Bhatia, Inder Preet Singh
,
Rajan, Amit
,
Hasvi, Jayaraj
في
Acidosis
,
Cardiac arrhythmia
,
Case reports
2024
Hypokalemic periodic paralysis (HPP) is an uncommon condition resulting from channelopathy, impacting skeletal muscles. It is distinguished by episodes of sudden and temporary muscle weakness alongside low potassium levels. The normalization of potassium resolves the associated paralysis. Most of these cases are hereditary. Few cases are acquired and are associated with an etiology related to endocrine disorders (e.g., thyrotoxicosis, hyperaldosteronism, and hypercortisolism). It is characterized by acute flaccid paralysis, usually of the ascending type, affecting the proximal region more than the distal region. Herein, we report the case of a 29-year-old male who instead of the ascending type presented with descending-type acute flaccid paralysis. Potassium level at presentation was 1.7 mEq/L. The patient was managed with parenteral and oral potassium supplementation, after which the weakness was completely resolved.
Journal Article
Constant Symplectic 2-groupoids
بواسطة
Rajan Amit Mehta
,
Tang, Xiang
2017
We propose a definition of symplectic 2-groupoid which includes integrations of Courant algebroids that have been recently constructed. We study in detail the simple but illustrative case of constant symplectic 2-groupoids. We show that the constant symplectic 2-groupoids are, up to equivalence, in one-to-one correspondence with a simple class of Courant algebroids that we call constant Courant algebroids. Furthermore, we find a correspondence between certain Dirac structures and Lagrangian sub-2-groupoids.
Paper
Modular Classes of Lie Groupoid Representations up to Homotopy
2015
We describe a construction of the modular class associated to a representation up to homotopy of a Lie groupoid. In the case of the adjoint representation up to homotopy, this class is the obstruction to the existence of a volume form, in the sense of Weinstein's \"The volume of a differentiable stack\".
Paper
Lie algebroid modules and representations up to homotopy
2014
We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaintrob's Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.
Paper
VB-groupoids and representation theory of Lie groupoids
2016
A VB-groupoid is a Lie groupoid equipped with a compatible linear structure. In this paper, we describe a correspondence, up to isomorphism, between VB-groupoids and 2-term representations up to homotopy of Lie groupoids. Under this correspondence, the tangent bundle of a Lie groupoid G corresponds to the \"adjoint representation\" of G. The value of this point of view is that the tangent bundle is canonical, whereas the adjoint representation is not. We define a cochain complex that is canonically associated to any VB-groupoid. The cohomology of this complex is isomorphic to the groupoid cohomology with values in the corresponding representations up to homotopy. When applied to the tangent bundle of a Lie groupoid, this construction produces a canonical complex that computes the cohomology with values in the adjoint representation. Finally, we give a classification of regular 2-term representations up to homotopy. By considering the adjoint representation, we find a new cohomological invariant associated to regular Lie groupoids.
Paper