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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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4 results for “anti-involution”

Symplectic groups over Lie subgroups of involutive algebrasmath.DG

New symplectic groups defined for Lie subgroups of algebras.

problem Defining new symplectic groups for Lie subgroups of algebras.

method Introducing symplectic group

\mathrm{Sp}_2(G, σ)

for Lie subgroups

G

of associative algebras

A

with anti-involution

σ

result New realizations of spin groups as

\mathrm{Sp}_2(G, σ)

for suitable subgroups

G

symplectic groups Lie subgroups algebras anti-involution spin groups

2025-10-13abs ↗pdf ↗

The hyperbolic moduli space of flat connections and the isomorphism of symplectic multiplicity spacesmath.DG

Let $G$ be a simple complex Lie group, $\alg{g}$ be its Lie algebra, $K$ be a maximal compact form of $G$ and $\alg{k}$ be a Lie algebra of $K$ . We denote by $X\rightarrow \overline{X}$ the anti-involution of $\alg{g}$ which singles out the compact form $\alg{k}$. Consider the space of flat $\alg{g}$-valued connections…

1996-03-29abs ↗pdf ↗

Minkowski superspaces and superstrings as almost real-complex supermanifoldsmath.DG

In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely different objects. They are what we call almost real-complex supermanifolds, i.e., real supermanifolds with a non-integrable distribution, the c…

2010-10-21abs ↗pdf ↗

Symplectic groups over noncommutative algebrasmath.DG

Introduces symplectic groups over noncommutative algebras and their geometric actions.

problem Understanding symplectic groups over noncommutative algebras.

method Introducing symplectic groups

\mathrm{Sp}_2(A,σ)

over noncommutative algebras and constructing geometric spaces.

result New insights into structure theory of classical Lie groups and construction of symmetric spaces.

symplectic groups noncommutative algebras geometric spaces Lie groups Hermitian algebras

2021-06-16abs ↗pdf ↗