Abstract
Let denote a field with The Racah algebra is the unital associative -algebra defined by generators and relations in the following way. The generators are A, B, C, D. The relations assert thatand each of the elementsis central in Additionally the element is central in In this paper, we explore the relationship between the Racah algebra and the universal enveloping algebra Let a, b, c denote mutually commuting indeterminates. We show that there exists a unique -algebra homomorphism that sendswhere x, y, z are the equitable generators for We additionally give the images of and certain Casimir elements of under We also show that the map is an injection and thus provides an embedding of into We use the injection to show that contains no zero divisors.
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