Complexity, Periodicity and One-Parameter Subgroups
Rolf Farnsteiner
TL;DR
This paper introduces a new numerical invariant for representations of infinitesimal group schemes using one-parameter subgroups, linking it to the module's complexity and period.
Contribution
It defines a novel invariant based on one-parameter subgroups and relates it to module complexity and periodicity for indecomposable modules.
Findings
Invariant relates to module period for complexity 1 modules
Provides a new tool to analyze representations of infinitesimal group schemes
Connects geometric subgroup data with algebraic module properties
Abstract
We use the variety of one-parameter subgroups to define a numerical invariant for a representation of an infinitesimal group scheme. For an indecomposable module M of complexity 1, this number is related to the period of M.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry