Jan G. Otterstrom F.

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QUANTUM GROUP

Werner Heisenberg startled science
in 1927 proving with certainty
uncertainty of knowing position
and momentum of a particle, today’s
probability space, irreducible
representation of a symmetry group
classical mechanics was replaced
formulating with non-commuting
operators, new notions of geometry
where coordinates do not commute
quantize groups, compositions
where all elements have inverses
generalize corresponding algebras
a familiarized world of similar objects.
Our term first appeared in theories
of Drinfeld and Jimbo as a class
of Hopf Algebras that can deform
into classical Lie Algebra Groups
multiple applications in realms like
topological invariants, tensor networks
benefiting from extra non-commutativity
are embedded, to grasp polynomial
invariants of knots, links and other things
like 3-manifold invariants to explore
mathematically our submersion
in a world, we feel but cannot see.




© Jan G. Otterstrom F. July 4, 2014