Blasiak, Pawel; Duchamp, Gerard H.E.; Solomon, Allan I.; Horzela, Andrzej and Penson, Karol A.
(2010).

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Abstract
We describe an algebra G of diagrams that faithfully gives a diagrammatic representation of the structures of both the Heisenberg–Weyl algebra H – the associative algebra of the creation and annihilation operators of quantum mechanics – and U(LH), the enveloping algebra of the Heisenberg Lie algebra LH. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also mirrored in the structure of U(LH). While both H and U(LH) are images of G, the algebra G has a richer structure and therefore embodies a finer combinatorial realization of the creation–annihilation system, of which it provides a concrete model.
Item Type:  Journal Item 

Copyright Holders:  2011 International Press 
ISSN:  10950753 
Academic Unit/School:  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences Faculty of Science, Technology, Engineering and Mathematics (STEM) 
Item ID:  29285 
Depositing User:  Astrid Peterkin 
Date Deposited:  22 Aug 2011 10:26 
Last Modified:  31 Oct 2017 05:21 
URI:  http://oro.open.ac.uk/id/eprint/29285 
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