Algebraic curves for commuting elements in the $q$-deformed Heisenberg algebra

• In this paper we extend the eliminant construction of Burchnall and Chaundy for commuting differential operators in the Heisenberg algebra to the q-deformed Heisenberg algebra and show that it again provides annihilating curves for commuting elements, provided q satisfies a natural condition. As a side result we obtain estimates on the dimensions of the eigenspaces of elements of this algebra in its faithful module of Laurent series.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

q-Deformed Heisenberg algebra

Commuting elements

Algebraic dependence

Eliminant

Mathematics/Applied Mathematics

matematik/tillämpad matematik

q-Deformed Heisenberg algebra

Commuting elements

Algebraic dependence

Eliminant

DIFFERENCE OPERATORS

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)