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Results tagged with ra.rings-and-algebras
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user 81895
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
3
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0
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Semisimple Lie algebras and the commutator algebra
Suppose $A$ is a associative unital $k$-algebra, where $\operatorname{char}k=0$. As is well-known, $A$ becomes a Lie algebra with respect to the commutator bracket $[x, y] = xy-yx$ for $x,y \in A$. Le …
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3
votes
On a dual of Kaplansky's $2^{nd}$ conjecture: admissible algebras?
In regards to your first question: I don't believe there is a way of telling in general whether or not an arbitrary algebra $A$ admits a Hopf structure. There are, however, in certain settings, some c …
- 426
11
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0
answers
402
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Lazard's theorem and Hopf structures on the polynomial algebra
Let $k$ be an algebraically closed field of characteristic $0$. A well-known result of Lazard's states that an algebraic group which is isomorphic as a variety to an affine space is unipotent (M. Laz …
- 426
6
votes
Accepted
Bialgebraic structure of Sklyanin algebra
In response to your first question, there is no Hopf structure on any Sklyanin algebra of any dimension. See Corollary 2.8 (i) of the following paper:
https://arxiv.org/pdf/1601.06687v1.pdf
- 426
3
votes
Classifying Hopf algebras that admit a single irreducible comodule
There have been several papers published on such Hopf algebras (which are referred to as "connected" Hopf algebras) over the past decade. In particular, over an algebraically closed field of character …
- 426