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- W3098435699 abstract "This paper examines the relationship between certain non-commutative analogues of projective 3-space, $mathbb{P}^3$, and the quantized enveloping algebras $U_q(mathfrak{sl}_2)$. The relationship is mediated by certain non-commutative graded algebras $S$, one for each $q in mathbb{C}^times$, having a degree-two central element $c$ such that $S[c^{-1}]_0 cong U_q(mathfrak{sl}_2)$. The non-commutative analogues of $mathbb{P}^3$ are the spaces $operatorname{Proj}_{nc}(S)$. We show how the points, fat points, lines, and quadrics, in $operatorname{Proj}_{nc}(S)$, and their incidence relations, correspond to finite dimensional irreducible representations of $U_q(mathfrak{sl}_2)$, Verma modules, annihilators of Verma modules, and homomorphisms between them." @default.
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- W3098435699 date "2018-01-01" @default.
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- W3098435699 title "Noncommutative geometry of homogenized quantum 𝔰𝔩(2, ℂ)" @default.
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- W3098435699 doi "https://doi.org/10.2140/pjm.2018.292.305" @default.
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