Noncommutative complete intersections

Kirkman, Ellen; Kuzmanovich, James; Zhang, J.J.

doi:10.1016/j.jalgebra.2014.12.046

Cited by 31 publications

(38 citation statements)

References 52 publications

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“…. , Ω n } is a regular sequence of normalizing homogeneous elements in C. In [KKZ4] we proposed calling a connected graded ring a cci, gci, or nci if the respective condition above holds for A; we called A a hypersurface if it is a cci when n = 1 (i.e. of the form C/(Ω), where C is a noetherian AS regular algebra and Ω is a regular, normal element of C).…”

Section: Special Linear Formentioning

confidence: 99%

See 1 more Smart Citation

Invariant theory of Artin-Schelter regular algebras: a survey

Kirkman¹

2016

Recent Developments in Representation Theory

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This is survey of results that extend notions of the classical invariant theory of linear actions by finite groups on k[x 1 , . . . , xn] to the setting of finite group or Hopf algebra H actions on an Artin-Schelter regular algebra A. We investigate when A H is AS regular, or AS Gorenstein, or a "complete intersection" in a sense that is defined. Directions of related research are explored briefly.

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Section: Special Linear Formentioning

confidence: 99%

“…If A satisfies (cci), then it satisfies (gci). [KKZ4,Example 6.3] shows that even both (gci) and (nci) together do not imply (cci), and [KKZ4,Example 6.2] shows that (gci) does not imply (nci).…”

Section: Special Linear Formentioning

confidence: 99%

Invariant theory of Artin-Schelter regular algebras: a survey

Kirkman¹

2016

Recent Developments in Representation Theory

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“…Hence, the analogous definition in the commutative setting is a special case of this last definition. Moreover, this definition is considered in [8] for algebras more general than S. The reader should perhaps also note that other notions of complete intersection exist in the literature, with most emphasizing a homological approach, such as the recent work in [6].…”

Section: Definitionmentioning

confidence: 99%

Corrigendum: Generalizations of graded Clifford algebras and of complete intersections

Cassidy

Vancliff

2014

Journal of the London Mathematical Society

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A correction is provided for Proposition 3.5 in the above‐mentioned article. The correction is: if S is a skew polynomial ring on finitely many generators of degree 1 that are normal elements in S, and if I is a homogeneous ideal of S that is generated by a normalizing sequence, then prefixdimdouble-struckkfalse(S/Ifalse) is finite if and only if S/I has no point modules and no fat point modules. A similar correction is provided for Corollary 3.6 of the same article.

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“…Question 0.7. Under the hypothesis of Theorem 0.3 (or more generally for a semisimple Hopf algebra H), is the covariant ring A cov H a complete intersection of GK type in the sense of [KKZ4]?…”

Section: Introductionmentioning

confidence: 99%