The Algebraic Approach to Duality: An Introduction

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00534685" target="_blank" >RIV/67985556:_____/20:00534685 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1142/9789811206092_0003" target="_blank" >http://dx.doi.org/10.1142/9789811206092_0003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/9789811206092_0003" target="_blank" >10.1142/9789811206092_0003</a>

Result language
angličtina
Original language name
The Algebraic Approach to Duality: An Introduction
Original language description
This survey article gives an elementary introduction to the algebraic approach to Markov process duality, as opposed to the pathwise ap- proach. In the algebraic approach, a Markov generator is written as the sum of products of simpler operators, which each have a dual with respect to some duality function. We discuss at length the recent sug- gestion by Giardinà, Redig, and others, that it may be a good idea to choose these simpler operators in such a way that they form an irreducible representation of some known Lie algebra. In particular, we collect the necessary background on representations of Lie algebras that is crucial for this approach. We also discuss older work by Lloyd and Sudbury on duality functions of product form and the relation between intertwining and duality.
Czech name
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Czech description
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Project
<a href="/en/project/GA16-15238S" target="_blank" >GA16-15238S: Collective behavior of large stochastic systems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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