Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

Authors:	Hudson RL; Pulmannova S

Institution:	Department of Mathematics, University of Nottingham, University Park Nottingham NG7 2RD, UK. E-mail: rlh{at}maths.nott.ac.uk Mathematical Institute, Slovak Academy of Sciences Bratislava, Slovakia. E-mail: pulmann{at}mau.savba.sk

Abstract:	The functional Ito formula, in the form df( ${Lambda}$ ) = f( ${Lambda}$ + d ${Lambda}$ ) –f( ${Lambda}$ ),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf( ${Lambda}$ ) + d( ${Lambda}$ ) – f( ${Lambda}$ ) is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f( ${Lambda}$ ) which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.

Keywords:	quantum stochastic calculus universal enveloping algebra chaotic decomposition
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