Nakayama Automorphism of Some Skew PBW Extensions

BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS

A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...

Jacobson’s conjecture and skew PBW extensions

The aim of this paper is to compute the Jacobson’s radical of skew PBW extensions over domains. As a consequence of this result we obtain a direct relation between these extensions and the Jacobson’s conjecture, which implies that skew PBW extensions over domains satisfy this conjecture.

Interactions between non-commutative algebraic geometry and skew PBW extensions

Skew quantum Murnaghan-Nakayama rule

In this extended abstract, we extend recent results of Assaf and McNamara, the skew Pieri rule and the skew Murnaghan-Nakayama rule, to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum function in terms of skew Schur functions. We give two proofs, one completely bijective in the spirit of Assaf-McNamara’s original proof, ...

extensions of some polynomial inequalities to the polar derivative

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