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Tagged with nilpotent-matrices rt.representation-theory
3 questions
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For a nilpotent matrix A, are the cardinalities of sets: 1) B: commute with A, 2) B: anticommute with A, 3) B: q-commute with A — the same?
Let us work over finite fields $F_{p^k}$. Simulations seems to indicate:
Question 1: Consider a nilpotent matrix $A$, consider the set of all matrices $B$, such that $AB-qBA=0$, then cardinality of ...
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About nilpotent Jordan algebras, matrix representations and formally real algebras
Given an non-commutative associative unital algebra A of characteristic $0$, one can construct a Jordan algebra $A+$ using the same underlying addition vector space.
Notice first that an associative ...
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About indecomposability and nilpotence
Transferred from MSE where it now received a complete answer.
Maybe the following is easy, but I am not an expert in finite-dimensional Lie algebras and was stuck on the following problem.
Can ...
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