On SAGBI bases theory of skew Poincaré-Birkhoff-Witt extensions

2025/08/14 by Suárez, Yésica, Reyes, Armando
#08A30 #13P10 #16S36 #16S38 #16Z05 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2508.10715

Abstract

In this paper we present a first approach toward a SAGBI bases theory of skew Poincaré-Birkhoff-Witt extensions, and investigate the problem of polynomial composition for SAGBI bases of subalgebras of these extensions.

Citations

• Description of bi-quadratic algebras on 3 generators with PBW basis
• Saturations of Subalgebras, SAGBI Bases, and U-invariants
• Filtered-graded transfer of noncommutative Gröbner bases
• Matrix computations on projective modules using noncommutative Gröbner bases
• Projective modules and Gröbner bases for skew PBW extensions
• Some homological properties of skew PBW extensions
• Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras
• Noncommutative Involutive Bases
• Theory of Non-Commutative Polynomials

Related

• Converting Subalgebra Bases with the Sagbi Walk
• Burchnall-Chaundy theory for skew Poincaré-Birkhoff-Witt extensions
• Sagbi bases, defining ideals and algebra of minors
• On NI and NJ skew PBW extensions
• On the annihilator condition for skew PBW extensions