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pro vyhledávání: '"Korepanov, Igor"'
Autor:
Korepanov, Igor G.
In this short note, we construct solutions to quantum tetrahedron equation of the kind "with variables on the edges". Each of these variables takes just two values, called sometimes "colors". We propose two different constructions. The first of them
Externí odkaz:
http://arxiv.org/abs/2404.13913
Autor:
Korepanov, Igor G.
A new version of the self-similarity spin transform on three-dimensional cubic lattices is proposed that makes possible calculation of nontrivial spin correlations in a "combinatorial" model, in which all permitted spin configurations have equal prob
Externí odkaz:
http://arxiv.org/abs/2402.12012
Autor:
Korepanov, Igor G.
A family of heptagon relations -- algebraic imitations of five-dimensional Pachner moves -- is constructed, parameterized by simplicial 3-cocycles. These relations are shown to possess a nontrivial "heptagon cohomology", which yields invariants of a
Externí odkaz:
http://arxiv.org/abs/2307.07774
Autor:
Korepanov, Igor G.
Publikováno v:
J. Math. Phys. 64, 101704 (2023)
Cubic blocks are studied assembled from linear operators $\mathcal R$ acting in the tensor product of $d$ linear "spin" spaces. Such operator is associated with a linear transformation $A$ in a vector space over a field $F$ of a finite characteristic
Externí odkaz:
http://arxiv.org/abs/2211.08926
Autor:
Korepanov, Igor G.
A cohomology theory for "odd polygon" relations -- algebraic imitations of Pachner moves in dimensions 3, 5, ... -- is constructed. Manifold invariants based on polygon relations and nontrivial polygon cocycles are proposed. Example calculation resul
Externí odkaz:
http://arxiv.org/abs/2205.00405
Autor:
Korepanov, Igor G.
A cohomology theory is proposed for the recently discovered heptagon relation -- an algebraic imitation of a 5-dimensional Pachner move 4--3. In particular, `quadratic cohomology' is introduced, and it is shown that it is quite nontrivial, and even m
Externí odkaz:
http://arxiv.org/abs/2110.08780
Autor:
Korepanov, Igor G.
Publikováno v:
In Partial Differential Equations in Applied Mathematics September 2024 11
Autor:
Korepanov, Igor G.
We construct a family of heptagon relations -- algebraic imitations of five-dimensional Pachner move 3--4, parameterized by simplicial 3-cocycles.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/2103.15159
Autor:
Dimakis, Aristophanes, Korepanov, Igor
Publikováno v:
J. Math. Phys. 62, 051701 (2021)
We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structure of (2n+1)-gon and 2n-simplex equations in direct sums of vector spa
Externí odkaz:
http://arxiv.org/abs/2009.02352
Autor:
Korepanov, Igor G.
Publikováno v:
Algebra i Analiz 33:4 (2021), 125--140 (Russian); St. Petersburg Math. J. 33 (2022), 675--686 (English)
An ansatz is proposed for heptagon relation, that is, algebraic imitation of five-dimensional Pachner move 4--3. Our relation is realized in terms of matrices acting in a direct sum of one-dimensional linear spaces corresponding to 4-faces.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/2003.10335