Graded Clifford Algebras of Prime Global Dimension with an Action ofHp

Laet, Kevin De

doi:10.1080/00927872.2014.942423

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…Remark For the case

m = 2

the equations for a Sklyanin algebra from example take on a particularly easy form

({, \begin{matrix} x y + y x + c z^{2} & = 0 \\ y z + z y + c x^{2} & = 0 \\ z x + x z + c y^{2} & = 0 \end{matrix})

where

c^{3} \neq 0, 1, - 8

, [, Theorem 3.1]. The case

c = 0

corresponds to an order associated to a so called skew polynomial algebra, and the ramification curve is a triangle of lines.…”

Section: Properties Of the Maximal Ordersmentioning

confidence: 99%

Construction of non-commutative surfaces with exceptional collections of length 4

Belmans

Presotto

2018

J. London Math. Soc.

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Recently de Thanhoffer de Völcsey and Van den Bergh classified the Euler forms on a free abelian group of rank 4 having the properties of the Euler form of a smooth projective surface. There are two types of solutions: one corresponding to double-struckP1×double-struckP1 (and non‐commutative quadrics), and an infinite family indexed by the natural numbers. For m=0,1 there are commutative and non‐commutative surfaces having this Euler form, whilst for m⩾2 there are no commutative surfaces. In this paper, we construct sheaves of maximal orders on surfaces having these Euler forms, giving a geometric construction for their numerical blowups.

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“…Remark For the case

m = 2

the equations for a Sklyanin algebra from example take on a particularly easy form

({, \begin{matrix} x y + y x + c z^{2} & = 0 \\ y z + z y + c x^{2} & = 0 \\ z x + x z + c y^{2} & = 0 \end{matrix})

where

c^{3} \neq 0, 1, - 8

, [, Theorem 3.1]. The case

c = 0

corresponds to an order associated to a so called skew polynomial algebra, and the ramification curve is a triangle of lines.…”

Section: Properties Of the Maximal Ordersmentioning

confidence: 99%

Construction of non-commutative surfaces with exceptional collections of length 4

Belmans

Presotto

2018

J. London Math. Soc.

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Constructing G-algebras

Laet

2016

Communications in Algebra

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Quotients of degenerate Sklyanin algebras

Laet

2017

J. Algebra Appl.

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Abstract. In this paper it is shown how the Heisenberg group of order 27 can be used to construct quotients of degenerate Sklyanin algebras. These quotients have properties similar to the classical Sklyanin case in the sense that they have the same Hilbert series, the same character series and a central element of degree 3. Regarding the central element of a 3-dimensional Sklyanin algebra, a better way to view this using Heisenberg-invariants is shown.

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Graded Clifford Algebras of Prime Global Dimension with an Action ofH_p

Cited by 3 publications

References 12 publications

Construction of non-commutative surfaces with exceptional collections of length 4

Construction of non-commutative surfaces with exceptional collections of length 4

Constructing G-algebras

Quotients of degenerate Sklyanin algebras

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