Quantum Heisenberg algebras are algebraic manifestations of Heisenberg’s Uncertainty Principle. Mathematically speaking, they are important examples of noncommutative algebras with “good” ring-theoretic properties. In this study, we look at both classical and quantum symmetries of said algebras. Specifically, in most cases, we are able to classify graded automorphisms, and we also extend these actions to generalized Taft algebras. This gives us an alternative way to realize actions on graded down-up algebras, which are important in both representation theory and noncommutative projective algebraic geometry.
Author(s): Benjamin Liber, Mathematics and Music Performance Major
Advisor(s): Jason Gaddis, Department of Mathematics
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