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Open-closed field algebras [PDF]

Commun. Math. Phys. 280, 207-261 (2008), 2006
We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a $\C$-extension of the Swiss-cheese partial operad.
B. Bakalov, G. Felder, H.S. Li, H.S. Li, H.S. Li, J. Cardy, J. Fjelstad, J. Fuchs, J. Fuchs, J. Fuchs, J. Fuchs, J. Fuchs, J. Fuchs, J. Fuchs, J.L. Cardy, J.L. Cardy, J.L. Cardy, J.L. Cardy, L. Kong, Liang Kong, M. Kontsevich, P. Etingof, P. Hu, V. Ostrik, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang, Y.-Z. Huang   +33 more
arxiv   +4 more sources

Connected Hopf Algebras of Dimension $p^2$ [PDF]

J. Algebra 391(2013) 93-113, 2012
Let $H$ be a finite-dimensional connected Hopf algebra over an algebraically closed field $\field$ of characteristic $p>0$. We provide the algebra structure of the associated graded Hopf algebra $\gr H$. Then, we study the case when $H$ is generated by a Hopf subalgebra $K$ and another element and the case when $H$ is cocommutative.
Andruskiewitsch, Andruskiewitsch, Demazure, Félix, Henderson, Humphreys, Isaacs, Jacobson, Montgomery, Quillen, Singer, Sweedler, Wang, Waterhouse, Xingting Wang, Ştefan   +15 more
arxiv   +3 more sources

A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus [PDF]

Entropy
We present a simple argument to derive the transformation of the quantum stochastic calculus formalism between inertial observers and derive the quantum open system dynamics for a system moving in a vacuum (or, more generally, a coherent) quantum field ...
John E. Gough
doaj   +2 more sources

A Study on Neutrosophic Algebra [PDF]

Neutrosophic Sets and Systems, 2022
The notion of neutrosophic algebra, ideal of neutrosophic algebra, kernel and neutrosophic quotient algebra have been proposed in this paper. We characterize some properties of neutrosophic algebra and proved that every quotient neutrosophic algebra is ...
T. Nagaiah, L. Bhaskar, P. Narasimha Swamy, Said Broumi   +3 more
doaj   +1 more source

Lie algebras of differentiations of linear algebras over a field

Дифференциальная геометрия многообразий фигур, 2021
In this paper, we study a system of linear equations that define the Lie algebra of differentiations DerA of an arbitrary finite-dimensional linear algebra over a field.
A. Ya. Sultanov, M.V. Glebova, O.V. Bolotnikova   +2 more
doaj   +1 more source

Differentiation of linear algebras with a unit over a field

Дифференциальная геометрия многообразий фигур, 2023
Linear algebras over a given field arise when studying various problems of algebra, analysis and geometry. The operation of differentiation, which originated in mathematical analysis, was transferred to the theory of linear algebras over a field, as well
A.Ya. Sultanov, M. V. Glebova, G. A. Sultanova   +2 more
doaj   +1 more source

Characteristic of Quaternion Algebra Over Fields

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023
Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space
Muhammad Faldiyan, Ema Carnia, Asep K. Supriatna   +2 more
doaj   +1 more source

Schneider-Teitelbaum duality for locally profinite groups [PDF]

Categories and General Algebraic Structures with Applications, 2021
We define monoidal structures on several categories of linear topological modules over the valuation ring of a local field, and study module theory with respect to the monoidal structures.
Tomoki Mihara
doaj   +1 more source

A class of continuous non-associative algebras arising from algebraic groups including $E_8$

Forum of Mathematics, Sigma, 2021
We give a construction that takes a simple linear algebraic group G over a field and produces a commutative, unital, and simple non-associative algebra A over that field.
Maurice Chayet, Skip Garibaldi
doaj   +1 more source

Nilpotent Lie algebras of derivations with the center of small corank

Karpatsʹkì Matematičnì Publìkacìï, 2020
Let $\mathbb K$ be a field of characteristic zero, $A$ be an integral domain over $\mathbb K$ with the field of fractions $R=Frac(A),$ and $Der_{\mathbb K}A$ be the Lie algebra of all $\mathbb K$-derivations on $A$. Let $W(A):=RDer_{\mathbb K} A$ and $L$
Y.Y. Chapovskyi, L.Z. Mashchenko, A.P. Petravchuk   +2 more
doaj   +1 more source