Symmetrization in tropical algebra
Location: Hill 705
Date & time: Wednesday, 20 January 2016 at 2:00PM - 2:11PM
Louis Rowen, Bar Ilan University: Tropicalization involves an ordered group, usually taken to be (R,+) or (Q,+), viewed as a semifield. Although there is a rich theory arising from this viewpoint, idempotent semirings possess a restricted algebraic structure theory, and also do not reflect important valuation-theoretic properties, thereby forcing researchers to rely often on combinatoric techniques.A max-plus algebra not only lacks negation, but it is not even additively cancellative. We introduce a general way to artificially insert negation, similar to group completion. This leads to the possibility of defining many auxiliary tropical structures, such as Lie algebras and exterior algebras, and also providing a key ingredient for a module theory that could enable one to use standard tools such as homology.