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Of all publications in the section: 318
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Working paper
Markarian N. math. arxive. Cornell University, 2015
Given a Lie algebra with a scalar product, one may consider the latter as a symplectic structure on a dg-scheme, which is the spectrum of the Chevalley--Eilenberg algebra. In the first section we explicitly calculate the first order deformation of the differential on the Hochschild complex of the Chevalley--Eilenberg algebra. The answer contains the Duflo character. This calculation is used in the last section. There we sketch the definition of the Wilson loop invariant of knots, which is hopefully equal to the Kontsevich integral, and show that for unknot they coincide. As a byproduct we get a new proof of the Duflo isomorphism for a Lie algebra with a scalar product.
Added: Sep 23, 2015
Working paper
Markaryan N. S. math. arxive. Cornell University, 2020
We apply Weyl n-algebras to prove formality theorems for higher Hochschild cohomology. We present two approaches: via propagators and via the factorization complex. It is shown that the second approach is equivalent to the first one taken with a new family of propagators we introduce.
Added: Oct 16, 2020
Working paper
Kaledin D. math. arxive. Cornell University, 2016
For every commutative ring A, one has a functorial commutative ring W(A) of p-typical Witt vectors of A, an iterated extension of A by itself. If A is not commutative, it has been known since the pioneering work of L. Hesselholt that W(A) is only an abelian group, not a ring, and it is an iterated extension of the Hochschild homology group HH0(A) by itself. It is natural to expect that this construction generalizes to higher degrees and arbitrary coefficients, so that one can define "Hochschild-Witt homology" WHH∗(A,M) for any bimodule M over an associative algebra A over a field k. Moreover, if one want the resulting theory to be a trace theory in the sense of arXiv:1308.3743, then it suffices to define it for A=k. This is what we do in this paper, for a perfect field k of positive characteristic p. Namely, we construct a sequence of polynomial functors Wm, m≥1 from k-vector spaces to abelian groups, related by restriction maps, we prove their basic properties such as the existence of Frobenius and Verschiebung maps, and we show that Wm are trace functors in the sense of arXiv:1308.3743. The construction is very simple, and it only depends on elementary properties of finite cyclic groups.
Added: Oct 29, 2016