# Bosonic realizations of the colour Heisenberg Lie algebra

@inproceedings{Sigurdsson2006BosonicRO, title={Bosonic realizations of the colour Heisenberg Lie algebra}, author={Gunnar Sigurdsson and Sergei D. Silvestrov}, year={2006} }

We describe realizations of the colour analogue of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to construct new operator representations of the colour Heisenberg Lie algebra. These representations are shown to be closely connected with some combinatorial identities and functional difference-differential interpolation formulae involving Euler numbers.

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VIEW 5 EXCERPTS

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 20 REFERENCES

## The Diamond Lemma for Power Series Algebras

VIEW 1 EXCERPT

## Commuting Elements in Q-Deformed Heisenberg Algebras

VIEW 1 EXCERPT

## On the classification of 3-dimensional coloured Lie algebras, in “Quantum Groups and Quantum Spaces

VIEW 2 EXCERPTS

## Representations of Commutation Relations. A Dynamical Systems Approach

VIEW 2 EXCERPTS

## Representations of the real forms of the graded analogue of the Lie algebra sl ( 2 , C )

## Representations of the real forms of the graded analogue of the Lie algebra sl(2,C), Ukrain

VIEW 3 EXCERPTS