6,403 research outputs found
On the compatibility between cup products, the Alekseev--Torossian connection and the Kashiwara--Vergne conjecture
For a finite-dimensional Lie algebra over a field , we deduce from the compatibility between cup products
Kontsevich (2003, Section 8) and from the main result of Shoikhet (2001) an
alternative way of re-writing Kontsevich product on by means of the Alekseev--Torossian flat connection (Alekseev
and Torossian, 2010). We deduce a similar formula directly from the
Kashiwara--Vergne conjecture (Kashiwara and Vergne, 1978).Comment: 8 pages, 1 figure; notation changed; corrected many other misprints
recently noticed; comments are very welcome
The explicit equivalence between the standard and the logarithmic star product for Lie algebras
The purpose of this short note is to establish an explicit equivalence
between the two star products and on the symmetric
algebra of a finite-dimensional Lie algebra over a field of characteristic 0 associated with
the standard angular propagator and the logarithmic one: the differential
operator of infinite order with constant coefficients realizing the equivalence
is related to the incarnation of the Grothendieck-Teichm\"uller group
considered by Kontsevich.Comment: 2 figures; corrected and completed the formulation of Theorem 3.7.
Comments are very welcome
Property, Legitimacy, Ideology: A Reality Check
Drawing on empirical evidence from history and anthropology, we aim to demonstrate that there is room for genealogical ideology critique within normative political theory. The test case is some libertarians’ use of folk notions of private property rights in defence of the legitimacy of capitalist states. Our genealogy of the notion of private property shows that asking whether a capitalist state can emerge without violations of self-ownership cannot help settling the question of its legitimacy, because the notion of private property presupposed by that question is a product of the entity it is supposed to help legitimise: the state. We anchor our genealogical critique in recent work on ideology in epistemology and philosophy of language, and in current debates on the methodology of political theory. But, unlike more traditional approaches that aim to debunk whole concepts or even belief systems, we propose a more targeted, argument-specific form of ideology critique
Deformation quantization with generators and relations
In this paper we prove a conjecture of B. Shoikhet which claims that two
quantization procedures arising from Fourier dual constructions actually
coincide.Comment: 9 pages; 4 figures; many typos have been corrected; the introduction
has been considerably extended and a more detailed exposition of the Koszul
theory behind the main idea has been added; the proof of Proposition 2.4
(iii) has been also extended; Subsection 3.2 has been enlarged, and a more
detailed exposition of how the Duflo element arises has been adde
Joint Optimal Pricing and Electrical Efficiency Enforcement for Rational Agents in Micro Grids
In electrical distribution grids, the constantly increasing number of power
generation devices based on renewables demands a transition from a centralized
to a distributed generation paradigm. In fact, power injection from Distributed
Energy Resources (DERs) can be selectively controlled to achieve other
objectives beyond supporting loads, such as the minimization of the power
losses along the distribution lines and the subsequent increase of the grid
hosting capacity. However, these technical achievements are only possible if
alongside electrical optimization schemes, a suitable market model is set up to
promote cooperation from the end users. In contrast with the existing
literature, where energy trading and electrical optimization of the grid are
often treated separately or the trading strategy is tailored to a specific
electrical optimization objective, in this work we consider their joint
optimization. Specifically, we present a multi-objective optimization problem
accounting for energy trading, where: 1) DERs try to maximize their profit,
resulting from selling their surplus energy, 2) the loads try to minimize their
expense, and 3) the main power supplier aims at maximizing the electrical grid
efficiency through a suitable discount policy. This optimization problem is
proved to be non convex, and an equivalent convex formulation is derived.
Centralized solutions are discussed first, and are subsequently distributed.
Numerical results to demonstrate the effectiveness of the so obtained optimal
policies are then presented
Loop observables for BF theories in any dimension and the cohomology of knots
A generalization of Wilson loop observables for BF theories in any dimension
is introduced in the Batalin-Vilkovisky framework. The expectation values of
these observables are cohomology classes of the space of imbeddings of a
circle. One of the resulting theories discussed in the paper has only trivalent
interactions and, irrespective of the actual dimension, looks like a
3-dimensional Chern-Simons theory.Comment: 13 page
A gerbe for the elliptic gamma function
The identities for elliptic gamma functions discovered by A. Varchenko and
one of us are generalized to an infinite set of identities for elliptic gamma
functions associated to pairs of planes in 3-dimensional space. The language of
stacks and gerbes gives a natural framework for a systematic description of
these identities and their domain of validity. A triptic curve is the quotient
of the complex plane by a subgroup of rank three (it is a stack). Our
identities can be summarized by saying that elliptic gamma functions form a
meromorphic section of a hermitian holomorphic abelian gerbe over the universal
oriented triptic curve.Comment: 54 page
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