Congenial algebras: extensions and examples. (English) Zbl 1470.16022
Summary: We study the congeniality property of algebras, as defined by Y. H. Bao et al. [Trans. Am. Math. Soc. 370, No. 12, 8613–8638 (2018; Zbl 1432.16011)], to establish a version of Auslander’s theorem for various families of filtered algebras. It is shown that the property is preserved under homomorphic images and tensor products under some mild conditions. Examples of congenial algebras in this paper include enveloping algebras of Lie superalgebras, iterated differential operator rings, quantized Weyl algebras, down-up algebras, and symplectic reflection algebras.
MSC:
| 16E65 | Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
| 16W70 | Filtered associative rings; filtrational and graded techniques |
| 16W22 | Actions of groups and semigroups; invariant theory (associative rings and algebras) |
| 17B35 | Universal enveloping (super)algebras |
Citations:
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