Previously enrolled in a nanotechnology degree at La Trobe University, Luke realised that his science subjects contained a running theme: the fundamentals lay within mathematics. Having knowledge in physics and chemistry without understanding the said fundamentals behind them did not bring great satisfaction from the learning process, so he transferred to a Bachelor of Science majoring in maths/stats with the intention of learning from purer subjects. As for the future, he is still trying to figure out the path to take from here on out.
Outside of formal academics he has interests in language, music, animation and video games, all of which he cannot help himself from analysing the small details and mechanics behind them which affect how they work as a whole.
Unital Associative Algebras over the Field ℝ and How They Relate to the Groups SU(2) and Spin(3)
The special unitary group of degree 2—SU(2)—and the group Spin(3) are said to be isomorphic to one another. This report displays this isomorphism in detail via their mutual isomorphism to the group of quaternions with norm equal to 1. However, since the definition of Spin(3) is reliant on the real Clifford algebras, a focus point of the report is on explaining these algebras generally while also displaying how a specific case of the real Clifford algebras, the quaternions, and an algebra associated to SU(2) are isomorphic unital associative algebras over the field ℝ.