Affine walled Brauer–Clifford superalgebras

Gao, Mengmeng; Rui, Hebing; Song, Linliang; Su, Yucai

doi:10.1016/j.jalgebra.2019.01.014

Cited by 5 publications

(12 citation statements)

References 17 publications

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“…On the other hand, if A = Cl is the two-dimensional Clifford superalgebra, then gl m|n (Cl) is isomorphic to the queer Lie superalgebra q(m + n), and our functors recover those defined in [BCK19]. As in the A = k case, these functors extend Schur-Weyl duality results for queer Lie superalgebras [Ser84b], actions of walled Brauer-Clifford superalgebras [JK14], and actions of affine walled Brauer-Clifford superalgebras [BCK19,GRSS19]. In fact, the Clifford superalgebra is the main example of interest where the Frobenius superalgebra is not symmetric.…”

Section: Introductionsupporting

confidence: 66%

Affine oriented Frobenius Brauer categories

McSween¹,

Savage²

2021

Preprint

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To any Frobenius superalgebra A we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer categeory. We define natural actions of these categories on categories of supermodules for general linear Lie superalgebras gl m|n (A) with entries in A. These actions generalize those on module categories for general linear Lie superalgebras and queer Lie superalgebras, which correspond to the cases where A is the ground field and the two-dimensional Clifford algebra, respectively.

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Section: Introductionsupporting

confidence: 66%

Affine oriented Frobenius Brauer categories

McSween¹,

Savage²

2021

Preprint

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“…, δ ⌊ℓ/2⌋ ∈ k, and define δ k for k > ⌊ℓ/2⌋ by (7.1). In [GRSS1,Definition 3.14] the cyclotomic walled Brauer-Clifford superalgebra BC ℓ,r,s is defined as the quotient of BC r,s by the additional relations f (x 1 ) = g(x 1 ) = 0 where g(t) is another monic degree ℓ polynomial satisfying certain conditions. One can check that those conditions imply f (x 1 ) and…”

Section: 2mentioning

confidence: 99%

A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

Brundan¹,

Comes²,

Kujawa³

2019

Can. J. Math.-J. Can. Math.

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We introduce the oriented Brauer-Clifford and degenerate affine oriented Brauer-Clifford supercategories. These are diagrammatically defined monoidal supercategories which provide combinatorial models for certain natural monoidal supercategories of supermodules and endosuperfunctors, respectively, for the Lie superalgebras of type Q. Our main results are basis theorems for these diagram supercategories. We also discuss connections and applications to the representation theory of the Lie superalgebra of type Q. 1

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“…10 we observe two scenarios: i) WMSN optimized according to method B with P ref = 0.01 and ii) Similar to i) but with P ref = 0.05. In both scenarios the trajectories of MSNs sharing the same path are synchronized and we set g = 8000, see (23).…”

Section: Simulations Resultsmentioning

confidence: 99%

“…where both g > 0 and P ref are the design parameters. The first term in (23) is the network ef f iciency while the second term is the penalization term. Regarding the penalization term note that: when g → +∞, the penalization term subtracts infinity to the optimization target ifP GP A > P ref but has negligible effect ifP GP A < P ref ; when v k → 0 the network efficiency tends to +∞ at the following rate 1/v 2 k but the penalization term tends to −∞ at an exponential rate (see (20), (21) and Fig.…”

Section: B Msn's Trajectory Configurationmentioning

confidence: 99%

“…In [21] the authors design a motion planning technique to make a team of robots escort a dynamic target by operating as a mobile virtual fencing which adapts its shape; in this case, the robots orbit around the target. Similar problems are considered in [22] and [23] To the best of our knowledge, the intruder detection literature dedicated to WMSN is scarce when compared to that dedicated to WSSN. Further, most of the existing work on WMSN for surveillance focus on the interior of the ROI rather than on the perimeter, and the few papers dealing with perimeter surveillance are mostly concerned with small perimeters.…”

Section: Introductionmentioning

confidence: 99%

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On Trajectory Design for Intruder Detection in Wireless Mobile Sensor Networks

Nurellari

Licea

Ghogho

et al. 2021

IEEE Trans. on Signal and Inf. Process. over Networks

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We address the problem of detecting the invasion of an intruder into a region of interest (ROI) which is monitored by a distributed bandwidth-constrained wireless mobile sensor network (WMSN). We design periodic trajectories for the mobile sensor nodes (MSNs) such that high detection probabilities are obtained while maintaining the MSNs' energy consumption low. To reduce the transmission and processing burden on the MSNs, we propose an operation algorithm based on two modes, surveying mode and conf irmation mode. In the former, to efficiently detect the intruder while using little mechanical energy, we optimize the surveying path such that the sensed area is maximized. During this mode, each MSN performs local detection and switches to the confirmation mode if and only if the intruder is suspected to be present. In the confirmation mode, each MSN collects further measurements over a predefined duration to reduce the detection uncertainly. A binary local hypothesis testing is performed at each MSN and only positive test statistics are transmitted to the FC where the ultimate decision is taken. Simulations results show the merits of the proposed two-mode operation algorithm in terms of detection performance and energy efficiency.

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Affine walled Brauer–Clifford superalgebras

Cited by 5 publications

References 17 publications

Affine oriented Frobenius Brauer categories

Affine oriented Frobenius Brauer categories

A Basis Theorem for the Degenerate Affine Oriented Brauer–Clifford Supercategory

On Trajectory Design for Intruder Detection in Wireless Mobile Sensor Networks

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