symmetric monoidal (∞,1)-category of spectra
Quantum nilpotent algebras are a class of associative algebras which are defined as iterated Ore extensions of a special type.
Let $K$ be a ground ring. An iterated Ore extension
where $\sigma_j$ is an automorphism of
and $\delta_j$ is the $\sigma_j$-derivation of $A_{j-1}$ is a quantum nilpotent algebra if it is equipped with a rational action of the torus $(K^\times)^l$ such that
$x_1,\ldots,x_n$ are eigenvectors of the action
each $\delta_j$ is a locally nilpotent $\sigma_j$-derivation of $A_{j-1}$
For every $j\in\{1,\ldots,n\}$, there exists $h_j\in (K^\times)^l$ such that $(h_j\cdot )|_{A_{j-1}} = \sigma_j$ and $h_j\cdot x_j = q_j x_j$ for some $q_j\in K^\times$ which is not a root of unity.
It follows that $\sigma_j\circ\delta_j = q_j \delta_j\sigma_j$ (this was stated as a requirement in the original definition).
Quantum nilpotent algebras are a framework where the so called derivative elimination algorithm can be applied.
Last revised on July 10, 2024 at 13:39:31. See the history of this page for a list of all contributions to it.