Trace formula for almost Lie algebra of operators |
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Authors: | Daoxing Xia |
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Institution: | (1) Mathematics Department, Vanderbilt University, 37235 Nashville, Tennessee |
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Abstract: | In this present paper, the almost Lie algebra of operators is introduced. By a natural homomorphism, this almost Lie algebra of operators is mapped to a Lie algebra. By choosing a basis in this Lie algebra, a bilinear functional on the enveloping algebra of this Lie algebra is defined through the trace of some operators which are related to the communtators. A general trace formula is obtained by means of the partial derivatives and symmetric operation in the enveloping algebra. More concrete formula is also obtained in terms of a linear functional on the commutators in some special cases. |
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