A Quantum Octonion Algebra
نویسندگان
چکیده
must be the field, two copies of the field, the split quaternions, or the split octonions. There is a natural q-version of the composition property that the algebra Oq of quantum octonions is shown to satisfy (see Prop. 4.12 below). We also prove that the quantum octonion algebra Oq satisfies the “q-Principle of Local Triality” (Prop. 3.12). Inside the quantum octonions are two nonisomorphic 4-dimensional subalgebras, which are q-deformations of the split quaternions. One of them is unital, and both of them give gl2 when considered as algebras under the commutator product [x, y] = x · y − y · x.
منابع مشابه
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