Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Structure of E6   We present the subalgebra structure of sl(3,O), a particular real form of E6
chosen for its relevance to particle physics through the connection between its
associated Lie group SL(3,O) and generalized Lorentz groups. Given the
complications related to the non-associativity of the octonions O and the
restriction to working with a real form of E6, we find that the traditional
methods used to study Lie algebras must be modified for our purposes. We use an
explicit representation of the Lie group SL(3,O) to produce the multiplication
table of the corresponding algebra sl(3,O). Both the multiplication table and
the group are then utilized to find subalgebras of sl(3,O). In particular, we
identify various subalgebras of the form sl(n, F) and su(n, F) within sl(3,O)
and we also find algebras corresponding to generalized Lorentz groups. Methods
based upon automorphisms of complex Lie algebras are developed to find less
obvious subalgebras of sl(3,O). While we focus on the subalgebra structure of
our real form of E6, these methods may also be used to study the subalgebra
structure of any other real form of E6. A maximal set of simultaneously
measurable observables in physics corresponds to a maximal set of Casimir
operators in the Lie algebra. We not only identify six Casimir operators in E6,
but produce a nested sequence of subalgebras and Casimir operators in E6
containing both su(3)+su(2)+u(1) corresponding to the Standard Model and the
Lorentz group of special relativity.

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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg