Heisenberg algebra

First we have a brief review on Heisenberg algebra and Clifford algebra and their representations. The general reference is [43, 9.13]... 

The infinite dimensional Heisenberg algebra s is a Lie algebra generated by p[m m E Z 0 ) and K with the following relations... 

It commutes with the action of the Heisenberg algebra 1). Hence (9.23) holds even for m or n = 0. 

The operator a i) in the Heisenberg algebra, of course, corresponds to the operator constructed in Chapter 8. But our commutator relation (8.14) differs from the standard one, we need to modify operators. In fact, it is more natural to change also the sign of the bilinear form. Hence we dehne... 

Heisenberg algebra and Hilbert schemes of points on projective surfaces, to appear in Ann. of... 

Another example of a three-dimensional Lie algebra is the Heisenberg algebra. This algebra consists of the set... 

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