Sergei Akbarov
Reputation
360
Top tag
Next privilege 500 Rep.
Access review queues
 Apr9 revised Analogs of the paralleloram identity in higher degrees formula Apr9 comment Analogs of the paralleloram identity in higher degrees Yes... differentiation can be defined inductively on polynomials... Qiaochu, anyway this formula (of polarization) is absurd, I don't like it. What is it called when a variable is not free and at the same time not bound in a formula? It seems to me I saw an explanation somewhere that this is not good... Apr9 revised Analogs of the paralleloram identity in higher degrees grammar Apr9 comment What are the analogs of quadratic forms of degree $k>2$? OK, I posted this as another question: math.stackexchange.com/questions/1226024/… Apr8 asked Analogs of the paralleloram identity in higher degrees Apr8 accepted What are the analogs of quadratic forms of degree $k>2$? Apr4 comment What are the analogs of quadratic forms of degree $k>2$? Qiaochu, I feel like a student with you. How does this polarization define "parallelogram identity", say, for cubic forms? Apr4 comment What are the analogs of quadratic forms of degree $k>2$? What I don't understand in this science: if quadratic forms have analogs in higher degrees, then there must be analogs of parallelogram identity for cubic forms, quartic froms, etc. What are they? Apr3 comment What are the analogs of quadratic forms of degree $k>2$? It will take me some time to find this book... Apr3 comment What are the analogs of quadratic forms of degree $k>2$? I need a reference... It's not good to invent a bicycle... Apr3 comment What are the analogs of quadratic forms of degree $k>2$? Qiaochu, I think it's not good to refer to books on jet bundles when mentioning these elementary facts. Do you know a textbook on algebra where this bijection between homogenious polynomials and symmetric multilinear forms is described? Apr3 comment What are the analogs of quadratic forms of degree $k>2$? "Algebraic form of degree $k$"? Apr3 revised What are the analogs of quadratic forms of degree $k>2$? edited title Apr3 comment What are the analogs of quadratic forms of degree $k>2$? @Shalop, for $k=2$ there is a theory that establishes a bijection between quadratic forms and symmetric bilinear forms. What is this theory for $k>2$? I even can't find any mentionings of these analogs of quadratic forms. Apr3 asked What are the analogs of quadratic forms of degree $k>2$? Feb25 comment Irreducible representations of $C(T,B(X))$ Thak you! Of course, I had in mind the unitary equivalence of representations! Feb25 accepted Irreducible representations of $C(T,B(X))$ Feb23 asked Irreducible representations of $C(T,B(X))$ Jan25 comment Is a matrix element of a norm continuous representation always a trigonometric polynomial? A trivial example: let $\sigma:G\to B(H)$ be a unitary irreducible representation, and $H^{\mathbb N}$ be the countable "Hilbert power of $H$". Then $\pi(t)(x_1,x_2,...)=(\sigma(t)x_1,\sigma(t)x_2,...)$ is a norm continuous irreducible representation of $G$. Shtern says that if we vary the power of $H$ (i.e. take different cardinal numbers instead of ${\mathbb N}$) and add a finite set of similar Hilbert powers, this will be a description of all norm continuous representations. Jan25 revised Is a matrix element of a norm continuous representation always a trigonometric polynomial? added 369 characters in body